Isoparametric finite element analysis of a generalized Robin boundary value problem on curved domains
(2009.11092)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 $L2$- and $H1$-norm. Numerical examples illustrate the theoretical results.
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