Isoparametric finite element analysis of a generalized Robin boundary value problem on curved domains
Dominik Edelmann · SMAI Journal of Computational Mathematics · 2021
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 L 2 - and H 1 -norm. Numerical examples illustrate the theoretical results.