Higher-order finite element methods for elliptic problems with interfaces
Numerical Analysis
2015-05-19 v1
Abstract
We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of the problem. We prove optimal error estimates of the methods on general quasi-uniform and shape regular meshes in maximum norms. In addition, we apply the method to a Stokes interface problem, adding correction terms for the velocity and the pressure, obtaining optimal convergence results.
Cite
@article{arxiv.1505.04347,
title = {Higher-order finite element methods for elliptic problems with interfaces},
author = {Johnny Guzman and Manuel A. Sanchez and Marcus Sarkis},
journal= {arXiv preprint arXiv:1505.04347},
year = {2015}
}
Comments
26 pages, 6 figures. An earlier version of this paper appeared on November 13, 2014 in http://www.brown.edu/research/projects/scientific-computing/reports/2014