Refactor Convergence tests for Beaminteraction with Lagrange Multipliers

[dharinib98]

Description

This is another post implementation issue of #637. The tests that use Lagrange Multipliers, right now use tolerances relaxed atleast by 6 orders. This could be improved by fixing how the residual is evaluated. Along similar lines, it would be helpful looking into field-wise convergence tests to be independent of scaling effects. See #1004

Possible Solution and Definition of Done

• Add convergence checks for Lagrange multipliers (see Add additional NOX status test for beaminteraction using Lagrange multipliers  #1660 )
• Switch to an incremental formulation for Lagrange multipliers (see Switch to incremental formulation for Lagrange Multipliers in Beaminteraction #1540 )
• Field-wise convergence tests ?

Interested Parties

@isteinbrecher @mayrmt @maxfirmbach

[mayrmt]

@dharinib98 As this issue came up again in #1501, we need to tackle it soon. Please look into it. @isteinbrecher and I are happy to discuss any open questions.