DPG approximation of eigenvalue problems
Numerical Analysis
2020-12-15 v1 Numerical Analysis
Abstract
In this paper, the discontinuous Petrov--Galerkin approximation of the Laplace eigenvalue problem is discussed. We consider in particular the primal and ultra weak formulations of the problem and prove the convergence together with a priori error estimates. Moreover, we propose two possible error estimators and perform the corresponding a posteriori error analysis. The theoretical results are confirmed numerically and it is shown that the error estimators can be used to design an optimally convergent adaptive scheme.
Cite
@article{arxiv.2012.06623,
title = {DPG approximation of eigenvalue problems},
author = {Fleurianne Bertrand and Daniele Boffi and Henrik Schneider},
journal= {arXiv preprint arXiv:2012.06623},
year = {2020}
}