Question on Maxwell eigenvalue FEM - Error estimation

1

Hello Fenics project community,

I have followed the implementation from the book “Jian-ming Jin - The finite element method in electromagnetics-John Wiley & Sons ( 2014)” for the Maxwell eigenvalue problem using Nedelec elements for the transversal field components and Lagrange elements for the longitudinal component.

My solver gives me initial good results for a cylindrical waveguide structure, but when I try to refine my mesh to improve my solution I cannot get to reduce the computed error in a consistent way.

I am using the following error estimator:

error_estimator.png

From: (Residual-based a posteriori error estimation for the Maxwell’s eigenvalue problem - By Daniele Boffi)

I select a number of mesh elements to be refined based on the error estimator, for which the global error that I obtain for each iteration does not decrease in a constant way.

Do you have any recommendations on what strategy could use for refining my mesh? Or what other type of error estimator could I use?

In advance, many thanks for your kind help and comments.

2

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