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Add HTML examples for various simulations
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‎examples/creepingFlowScript/README.md‎

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This example solves a 2D lid-driven cavity flow using the creeping flow solver with Taylor-Hood (Q2-Q1) elements. For detailed information on the model setup, refer to the corresponding [tutorial](https://feascript.com/tutorials/lid-driven-cavity-2d-creeping-flow.html) on the FEAScript website.
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## Running the Examples
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## HTML Examples
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Each example also includes an HTML variant (e.g., `lidDrivenCavity2DCreepingFlow.html`) that runs the same simulation in the browser with built-in visualization using Plotly.js. Simply open the HTML file in a web browser to run.
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## Running the Node.js Examples
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#### 1. Create package.json with ES module support:
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‎examples/creepingFlowScript/lidDrivenCavity2DCreepingFlow/lidDrivenCavity2DCreepingFlow.html‎

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<!DOCTYPE html>
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<!--
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════════════════════════════════════════════════════════════════
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FEAScript Core Library
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Lightweight Finite Element Simulation in JavaScript
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Version: 0.2.0 | https://feascript.com
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MIT License © 2023–2026 FEAScript
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════════════════════════════════════════════════════════════════
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-->
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<html>
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<head>
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<title>FEAScript Example: Lid-Driven Cavity 2D Creeping Flow</title>
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<meta charset="UTF-8" />
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<!-- Link to the CSS files -->
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<link href="https://feascript.com/feascript-website.css" rel="stylesheet" type="text/css" />
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<link href="https://fonts.googleapis.com/css2?family=Roboto:wght@400;700&display=swap" rel="stylesheet" />
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<!-- Import the Math.js library for mathematical operations -->
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<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjs/11.12.0/math.min.js"></script>
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<!-- Import the Plotly.js library for plotting -->
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<script src="https://cdnjs.cloudflare.com/ajax/libs/plotly.js/2.35.3/plotly.min.js"></script>
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</head>
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<body>
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<h2>Lid-Driven Cavity 2D Creeping Flow</h2>
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<h3>Velocity Magnitude</h3>
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<div id="velocityMagnitudeCanvas"></div>
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<h3>u-Velocity Component</h3>
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<div id="uVelocityCanvas"></div>
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<h3>v-Velocity Component</h3>
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<div id="vVelocityCanvas"></div>
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<script type="module">
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// Import FEAScript library
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import { FEAScriptModel, plotSolution, printVersion } from "https://core.feascript.com/dist/feascript.esm.js";
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// import { FEAScriptModel, plotSolution, printVersion } from "../../../src/index.js";
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window.addEventListener("DOMContentLoaded", () => {
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console.log("FEAScript Version:", printVersion);
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// Create a new FEAScript model
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const model = new FEAScriptModel();
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// Select physics/PDE
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model.setModelConfig("creepingFlowScript");
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// Define mesh configuration
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model.setMeshConfig({
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meshDimension: "2D",
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elementOrder: "quadratic",
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numElementsX: 12,
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numElementsY: 6,
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maxX: 4,
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maxY: 2,
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});
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// Define boundary conditions
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model.addBoundaryCondition("0", ["constantVelocity", 0, 0]); // Bottom boundary
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model.addBoundaryCondition("1", ["constantVelocity", 0, 0]); // Left boundary
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model.addBoundaryCondition("2", ["constantVelocity", 1, 0]); // Top boundary
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model.addBoundaryCondition("3", ["constantVelocity", 0, 0]); // Right boundary
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// Set solver method
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model.setSolverMethod("lusolve");
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// Solve the problem
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const result = model.solve();
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// Print results to console
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console.log(`Number of nodes in mesh: ${result.nodesCoordinates.nodesXCoordinates.length}`);
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console.log("Solution vector:", result.solutionVector);
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// Extract velocity and pressure fields from the solution vector
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// DOF layout: [u₀…u_{N₂−1}, v₀…v_{N₂−1}, p₀…p_{N₁−1}]
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const totalNodesVelocity = model._creepingFlowMetadata.totalNodesVelocity;
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const solutionVector = result.solutionVector;
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const uVelocity = solutionVector.slice(0, totalNodesVelocity);
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const vVelocity = solutionVector.slice(totalNodesVelocity, 2 * totalNodesVelocity);
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const velocityMagnitude = uVelocity.map((u, i) => Math.sqrt(u * u + vVelocity[i] * vVelocity[i]));
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// Plot velocity magnitude as a 2D contour plot
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plotSolution(
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model,
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{ solutionVector: velocityMagnitude, nodesCoordinates: result.nodesCoordinates },
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"contour",
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"velocityMagnitudeCanvas"
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);
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// Plot u-velocity component as a 2D contour plot
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plotSolution(
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model,
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{ solutionVector: uVelocity, nodesCoordinates: result.nodesCoordinates },
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"contour",
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"uVelocityCanvas"
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);
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// Plot v-velocity component as a 2D contour plot
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plotSolution(
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model,
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{ solutionVector: vVelocity, nodesCoordinates: result.nodesCoordinates },
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"contour",
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"vVelocityCanvas"
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);
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});
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</script>
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</body>
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</html>

‎examples/frontPropagationScript/README.md‎

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This example demonstrates solving an eikonal equation in a 2D domain to track the movement of a solidification interface. For detailed information on the model setup, refer to the corresponding [tutorial](https://feascript.com/tutorials/solidification-front-2d.html) in the FEAScript website.
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## Running the Examples
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## HTML Examples
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Each example also includes an HTML variant (e.g., `solidificationFront2D.html`) that runs the same simulation in the browser with built-in visualization using Plotly.js. Simply open the HTML file in a web browser to run.
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## Running the Node.js Examples
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#### 1. Create package.json with ES module support:
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‎examples/frontPropagationScript/solidificationFront2D/solidificationFront2D.html‎

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<!DOCTYPE html>
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<!--
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════════════════════════════════════════════════════════════════
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FEAScript Core Library
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Lightweight Finite Element Simulation in JavaScript
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Version: 0.2.0 | https://feascript.com
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MIT License © 2023–2026 FEAScript
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════════════════════════════════════════════════════════════════
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-->
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<html>
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<head>
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<title>FEAScript Example: Solidification Front 2D</title>
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<meta charset="UTF-8" />
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<!-- Link to the CSS files -->
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<link href="https://feascript.com/feascript-website.css" rel="stylesheet" type="text/css" />
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<link href="https://fonts.googleapis.com/css2?family=Roboto:wght@400;700&display=swap" rel="stylesheet" />
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<!-- Import the Math.js library for mathematical operations -->
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<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjs/11.12.0/math.min.js"></script>
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<!-- Import the Plotly.js library for plotting -->
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<script src="https://cdnjs.cloudflare.com/ajax/libs/plotly.js/2.35.3/plotly.min.js"></script>
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</head>
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<body>
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<h2>Solidification Front 2D</h2>
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<!-- Container element where the solution plot will be rendered -->
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<div id="resultsCanvas"></div>
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<script type="module">
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// Import FEAScript library
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import { FEAScriptModel, plotSolution, printVersion } from "https://core.feascript.com/dist/feascript.esm.js";
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// import { FEAScriptModel, plotSolution, printVersion } from "../../../src/index.js";
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window.addEventListener("DOMContentLoaded", () => {
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console.log("FEAScript Version:", printVersion);
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// Create a new FEAScript model
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const model = new FEAScriptModel();
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// Select physics/PDE
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model.setModelConfig("frontPropagationScript");
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// Define mesh configuration
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model.setMeshConfig({
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meshDimension: "2D",
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elementOrder: "quadratic",
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numElementsX: 12,
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numElementsY: 8,
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maxX: 4,
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maxY: 2,
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});
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// Define boundary conditions
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model.addBoundaryCondition("0", ["constantValue", 0]); // Bottom boundary
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model.addBoundaryCondition("1", ["constantValue", 0]); // Left boundary
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model.addBoundaryCondition("2", ["zeroGradient"]); // Top boundary
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model.addBoundaryCondition("3", ["constantValue", 0]); // Right boundary
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// Set solver method
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model.setSolverMethod("lusolve");
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// Solve the problem
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const result = model.solve();
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// Print results to console
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console.log(`Number of nodes in mesh: ${result.nodesCoordinates.nodesXCoordinates.length}`);
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console.log("Solution vector:", result.solutionVector);
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// Plot the solution as a 2D contour plot
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plotSolution(model, result, "contour", "resultsCanvas");
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});
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</script>
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</body>
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</html>

‎examples/generalFormPDEScript/README.md‎

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This example demonstrates solving a one-dimensional advection-diffusion problem with a Gaussian source term. The problem models the transport of a substance under the effects of both diffusion and advection. For detailed information on the model setup, refer to the corresponding [tutorial](https://feascript.com/tutorials/advection-diffusion-1d.html) in the FEAScript website.
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## Running the Examples
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## HTML Examples
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Each example also includes an HTML variant (e.g., `advectionDiffusion1D.html`) that runs the same simulation in the browser with built-in visualization using Plotly.js. Simply open the HTML file in a web browser to run.
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## Running the Node.js Examples
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#### 1. Create package.json with ES module support:
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‎examples/generalFormPDEScript/advectionDiffusion1D/advectionDiffusion1D.html‎

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<!DOCTYPE html>
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<!--
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════════════════════════════════════════════════════════════════
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FEAScript Core Library
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Lightweight Finite Element Simulation in JavaScript
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Version: 0.2.0 | https://feascript.com
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MIT License © 2023–2026 FEAScript
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════════════════════════════════════════════════════════════════
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-->
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<html>
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<head>
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<title>FEAScript Example: Advection-Diffusion 1D</title>
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<meta charset="UTF-8" />
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<!-- Link to the CSS files -->
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<link href="https://feascript.com/feascript-website.css" rel="stylesheet" type="text/css" />
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<link href="https://fonts.googleapis.com/css2?family=Roboto:wght@400;700&display=swap" rel="stylesheet" />
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<!-- Import the Math.js library for mathematical operations -->
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<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjs/11.12.0/math.min.js"></script>
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<!-- Import the Plotly.js library for plotting -->
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<script src="https://cdnjs.cloudflare.com/ajax/libs/plotly.js/2.35.3/plotly.min.js"></script>
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</head>
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<body>
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<h2>Advection-Diffusion 1D</h2>
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<!-- Container element where the solution plot will be rendered -->
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<div id="resultsCanvas"></div>
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<script type="module">
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// Import FEAScript library
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import { FEAScriptModel, plotSolution, printVersion } from "https://core.feascript.com/dist/feascript.esm.js";
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// import { FEAScriptModel, plotSolution, printVersion } from "../../../src/index.js";
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window.addEventListener("DOMContentLoaded", () => {
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console.log("FEAScript Version:", printVersion);
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// Create a new FEAScript model
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const model = new FEAScriptModel();
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// Select physics/PDE
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model.setModelConfig("generalFormPDEScript", {
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coefficientFunctions: {
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// Equation d²u/dx² - 10 du/dx = 10 * exp(-200 * (x - 0.5)²)
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A: (x) => 1, // Diffusion coefficient
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B: (x) => -10, // Advection coefficient
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C: (x) => 0, // Reaction coefficient
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D: (x) => 10 * Math.exp(-200 * Math.pow(x - 0.5, 2)), // Source term
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},
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});
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// Define mesh configuration
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model.setMeshConfig({
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meshDimension: "1D",
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elementOrder: "quadratic",
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numElementsX: 20,
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maxX: 1.0,
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});
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// Define boundary conditions
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model.addBoundaryCondition("0", ["constantValue", 1]); // Left boundary
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model.addBoundaryCondition("1", "zeroGradient"); // Right boundary
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// Set solver method
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model.setSolverMethod("lusolve");
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// Solve the problem
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const result = model.solve();
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// Print results to console
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console.log(`Number of nodes in mesh: ${result.nodesCoordinates.nodesXCoordinates.length}`);
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console.log("Solution vector:", result.solutionVector);
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// Plot the solution as a 1D line plot
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plotSolution(model, result, "line", "resultsCanvas");
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});
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</script>
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</body>
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</html>

‎examples/heatConductionScript/README.md‎

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For detailed information on the model setup, refer to the corresponding [tutorial](https://feascript.com/tutorials/heat-conduction-2d-rhom-fin-gmsh.html) in the FEAScript website.
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## Running the Examples
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## HTML Examples
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Each example also includes an HTML variant (e.g., `heatConduction1DWall.html`, `heatConduction2DFin.html`) that runs the same simulation in the browser with built-in visualization using Plotly.js. Simply open the HTML file in a web browser to run.
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## Running the Node.js Examples
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#### 1. Create package.json with ES module support:
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‎examples/heatConductionScript/heatConduction1DWall/heatConduction1DWall.html‎

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<!DOCTYPE html>
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<!--
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════════════════════════════════════════════════════════════════
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FEAScript Core Library
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Lightweight Finite Element Simulation in JavaScript
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Version: 0.2.0 | https://feascript.com
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MIT License © 2023–2026 FEAScript
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════════════════════════════════════════════════════════════════
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-->
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<html>
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<head>
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<title>FEAScript Example: Heat Conduction 1D Wall</title>
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<meta charset="UTF-8" />
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<!-- Link to the CSS files -->
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<link href="https://feascript.com/feascript-website.css" rel="stylesheet" type="text/css" />
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<link href="https://fonts.googleapis.com/css2?family=Roboto:wght@400;700&display=swap" rel="stylesheet" />
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<!-- Import the Math.js library for mathematical operations -->
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<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjs/11.12.0/math.min.js"></script>
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<!-- Import the Plotly.js library for plotting -->
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<script src="https://cdnjs.cloudflare.com/ajax/libs/plotly.js/2.35.3/plotly.min.js"></script>
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</head>
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<body>
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<h2>Heat Conduction 1D Wall</h2>
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<!-- Container element where the solution plot will be rendered -->
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<div id="resultsCanvas"></div>
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<script type="module">
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// Import FEAScript library
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import { FEAScriptModel, plotSolution, printVersion } from "https://core.feascript.com/dist/feascript.esm.js";
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// import { FEAScriptModel, plotSolution, printVersion } from "../../../src/index.js";
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window.addEventListener("DOMContentLoaded", () => {
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console.log("FEAScript Version:", printVersion);
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// Create a new FEAScript model
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const model = new FEAScriptModel();
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// Select physics/PDE
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model.setModelConfig("heatConductionScript");
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// Define mesh configuration
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model.setMeshConfig({
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meshDimension: "1D",
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elementOrder: "linear",
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numElementsX: 10,
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maxX: 0.15,
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});
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// Define boundary conditions
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model.addBoundaryCondition("0", ["convection", 1, 25]); // Left boundary
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model.addBoundaryCondition("1", ["constantTemp", 5]); // Right boundary
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// Set solver method
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model.setSolverMethod("lusolve");
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// Solve the problem
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const result = model.solve();
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// Print results to console
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console.log(`Number of nodes: ${result.nodesCoordinates.nodesXCoordinates.length}`);
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console.log("Solution vector:", result.solutionVector);
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// Plot the solution as a 1D line plot
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plotSolution(model, result, "line", "resultsCanvas");
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});
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</script>
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</body>
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</html>

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