Isoparametric finite element analysis of a generalized Robin boundary value problem on curved domains
Edelmann, Dominik1
1 Mathematisches Institut, Universität Tübingen, Germany
The SMAI Journal of computational mathematics, Tome 7 (2021), pp. 57-73.

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.

Publié le :
DOI : 10.5802/smai-jcm.71
Mots clés : generalized Robin boundary conditions, Laplace–Beltrami operator, isoparametric finite elements, finite element method, error analysis
Edelmann, Dominik 1

1 Mathematisches Institut, Universität Tübingen, Germany 
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     title = {Isoparametric finite element analysis of a generalized  {Robin} boundary value problem on curved domains},
     journal = {The SMAI Journal of computational mathematics},
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     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
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Edelmann, Dominik. Isoparametric finite element analysis of a generalized  Robin boundary value problem on curved domains. The SMAI Journal of computational mathematics, Tome 7 (2021), pp. 57-73. doi : 10.5802/smai-jcm.71. http://www.numdam.org/articles/10.5802/smai-jcm.71/

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