Isoparametric finite element analysis of a generalized Robin boundary value problem on curved domains
Numerical Analysis
2020-09-24 v1 Numerical Analysis
Abstract
We study the discretization of an elliptic partial differential equation, posed on a two- or three-dimensional domain with smooth boundary, endowed with a generalized Robin boundary condition which involves the Laplace-Beltrami operator on the boundary surface. The boundary is approximated with piecewise polynomial faces and we use isoparametric finite elements of arbitrary order for the discretization. We derive optimal-order error bounds for this non-conforming finite element method in both - and -norm. Numerical examples illustrate the theoretical results.
Keywords
Cite
@article{arxiv.2009.11092,
title = {Isoparametric finite element analysis of a generalized Robin boundary value problem on curved domains},
author = {Dominik Edelmann},
journal= {arXiv preprint arXiv:2009.11092},
year = {2020}
}