I have completed a 2D finite difference code in MATLAB that has a domain of (0,1)x(0,1) and has Dirichlet Boundary Conditions of value zero along the boundary. I get convergence rates of 2 for second order and 4 for fourth order. My issue now is that I'm now wanting to change the domain to a more complex domain and see the resulting convergence rates. I have cut 4 square holes throughout the plate within the domain (0,1)x(0,1) with Dirichlet Boundary Conditions of value zero. When I run the code for the new domain I do not get convergence rates of 2 and 4. They usually end up being in the 1.3 - 2 range. I'm imposing the inner boundary conditions using the penalty method.(adsbygoogle = window.adsbygoogle || []).push({});

It is my belief that the holes within the new domain are causing the convergence rates to change. Is there a reason for this or is something just incorrect in my calculations? I have made sure the code was correct using the method of manufactured solutions.

Attached is example domain and solution output.

I can attach the code if needed but I'm more so asking a theory question I suppose

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# A 2D Finite Difference Convergence Rate Issues

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