A linear nonconforming finite element method for Maxwells equations in two dimensions. Part I: Frequency domain
We suggest a linear nonconforming triangular element for Maxwells equations and test it in the context of the vector Helmholtz equation. The element uses discontinuous normal fields and tangential fields with continuity at the midpoint of the element sides, an approximation related to the CrouzeixRaviart element for Stokes. The element is stabilized using the jump of the tangential fields, giving us a free parameter to decide. We give dispersion relations for different stability parameters and give some numerical examples, where the results converge quadratically with the mesh size for problems with smooth boundaries. The proposed element is free from spurious solutions and, for cavity eigenvalue problems, the eigenfrequencies that correspond to well-resolved eigenmodes are reproduced with the correct multiplicity.
finite element maxwells equations stabilized methods interior penalty method nonconforming method