Convergence on layer-adapted meshes and anisotropic interpolation error estimates of non-standard higher order finite elements

Authors:
Sebastian Franz;Gunar Matthies
Affiliations:
Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland;Universität Kassel, Fachbereich 10 Mathematik und Naturwissenschaften, Institut für Mathematik, Heinrich-Plett-Straíe 40, 34132 Kassel, Germany
Venue:
Applied Numerical Mathematics
Year:
2011

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Abstract

For a general class of finite element spaces based on local polynomial spaces E with P"p@?E@?Q"p we construct a vertex-edge-cell and point-value oriented interpolation operators that fulfil anisotropic interpolation error estimates. Using these estimates we prove @e-uniform convergence of order p for the Galerkin FEM and the LPSFEM for a singularly perturbed convection-diffusion problem with characteristic boundary layers.