%0 Journal Article %1 burman2019finite %A Burman, Erik %A Hansbo, Peter %A Larson, Mats G. %A Larsson, Karl %A Massing, André %D 2019 %J Numerische Mathematik %K 65n30-pdes-bvps-finite-elements %N 1 %P 141-172 %R 10.1007/s00211-018-0990-2 %T Finite element approximation of the Laplace-Beltrami operator on a surface with boundary. %U https://link.springer.com/article/10.1007/s00211-018-0990-2 %V 141 %X We develop a finite element method for the Laplace–Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced weakly using Nitsche’s method. We prove optimal order a priori error estimates for piecewise continuous polynomials of order k≥1 in the energy and L2 norms that take the approximation of the surface and the boundary into account.

@article{burman2019finite, abstract = {We develop a finite element method for the Laplace–Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced weakly using Nitsche’s method. We prove optimal order a priori error estimates for piecewise continuous polynomials of order k≥1 in the energy and L2 norms that take the approximation of the surface and the boundary into account.}, added-at = {2023-07-11T00:45:39.000+0200}, author = {Burman, Erik and Hansbo, Peter and Larson, Mats G. and Larsson, Karl and Massing, André}, biburl = {https://www.bibsonomy.org/bibtex/2297f7206d30247cceb8eca8a72ad1e55/gdmcbain}, doi = {10.1007/s00211-018-0990-2}, ee = {https://www.wikidata.org/entity/Q92582406}, interhash = {0f7b43d156680e8fdb96d724c9a42032}, intrahash = {297f7206d30247cceb8eca8a72ad1e55}, journal = {Numerische Mathematik}, keywords = {65n30-pdes-bvps-finite-elements}, number = 1, pages = {141-172}, timestamp = {2023-07-11T00:45:39.000+0200}, title = {Finite element approximation of the Laplace-Beltrami operator on a surface with boundary.}, url = {https://link.springer.com/article/10.1007/s00211-018-0990-2}, volume = 141, year = 2019 }