An adaptive mesh refinement strategy to ensure quasi-optimality of finite element methods for self-adjoint Helmholtz problems
Numerical Analysis
2024-12-31 v3 Numerical Analysis
Abstract
It is well known that the quasi-optimality of the Galerkin finite element method for the Helmholtz equation is dependent on the mesh size and the wave-number. In the literature, different criteria have been proposed to ensure uniform quasi-optimality of the discretisation. In the present work, we study the uniform quasi-optimality of conforming and non-conforming Crouzeix-Raviart discretisation of the self-adjoint Helmholtz problem. In particular, we propose an adaptive scheme, coupled with a residual-based indicator, for generating guaranteed quasi-optimal meshes with minimal degrees of freedom.
Keywords
Cite
@article{arxiv.2403.06266,
title = {An adaptive mesh refinement strategy to ensure quasi-optimality of finite element methods for self-adjoint Helmholtz problems},
author = {Tim van Beeck and Umberto Zerbinati},
journal= {arXiv preprint arXiv:2403.06266},
year = {2024}
}