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Update SBP docs with convergence references #265

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JoshuaLampert merged 1 commit into from
Nov 24, 2025
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Update SBP docs with convergence references #265

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11 changes: 11 additions & 0 deletions docs/src/SBP_Operators.md
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Expand Up @@ -117,6 +117,17 @@ M = \Delta x \cdot \text{diag}(1/2, 1, 1, \ldots, 1, 1/2)
```

You can verify that this satisfies the SBP property and provides second-order accuracy in the interior with first-order accuracy at the boundaries.
Thus, under standard assumptions, one can prove that this SBP operator leads to methods with order of convergence two (in the discrete ``L^2`` norm induced by the mass matrix).[^SvärdNordström2019][^SvärdNordström2021]

[^SvärdNordström2019]:
Svärd, Nordström (2019):
On the convergence rates of energy-stable finite-difference schemes
[DOI: 10.1016/j.jcp.2019.07.018](https://doi.org/10.1016/j.jcp.2019.07.018)

[^SvärdNordström2021]:
Svärd, Nordström (2021):
Convergence of energy stable finite-difference schemes with interfaces
[DOI: 10.1016/j.jcp.2020.110020](https://doi.org/10.1016/j.jcp.2020.110020)

## 3. Types of SBP Operators

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