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Convergence on layer-adapted meshes and anisotropic interpolation error estimates of non-standard higher order finite elements |
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| Authors: | Sebastian Franz Gunar Matthies |
| Institution: | a Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland b Universität Kassel, Fachbereich 10 Mathematik und Naturwissenschaften, Institut für Mathematik, Heinrich-Plett-Straße 40, 34132 Kassel, Germany |
| Abstract: | For a general class of finite element spaces based on local polynomial spaces E with Pp⊂E⊂Qp we construct a vertex-edge-cell and point-value oriented interpolation operators that fulfil anisotropic interpolation error estimates.Using these estimates we prove ε-uniform convergence of order p for the Galerkin FEM and the LPSFEM for a singularly perturbed convection-diffusion problem with characteristic boundary layers. |
| Keywords: | Singular perturbation Characteristic layers Exponential layers Shishkin meshes Local-projection Higher order FEM |
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