English

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 L2L^2- and H1H^1-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}
}