DPG methods for a fourth-order div problem
Numerical Analysis
2022-01-03 v1 Numerical Analysis
Abstract
We study a fourth-order div problem and its approximation by the discontinuous Petrov-Galerkin method with optimal test functions. We present two variants, based on first and second-order systems. In both cases we prove well-posedness of the formulation and quasi-optimal convergence of the approximation. Our analysis includes the fully-discrete schemes with approximated test functions, for general dimension and polynomial degree in the first-order case, and for two dimensions and lowest-order approximation in the second-order case. Numerical results illustrate the performance for quasi-uniform and adaptively refined meshes.
Cite
@article{arxiv.2112.15153,
title = {DPG methods for a fourth-order div problem},
author = {Thomas Führer and Pablo Herrera and Norbert Heuer},
journal= {arXiv preprint arXiv:2112.15153},
year = {2022}
}
Comments
Supported by ANID-Chile through FONDECYT projects 1190009, 1210391