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

Authors
Journal
Applied Numerical Mathematics
0168-9274
Publisher
Elsevier
Publication Date
Volume
61
Issue
6
Identifiers
DOI: 10.1016/j.apnum.2011.02.001
Keywords
  • Singular Perturbation
  • Characteristic Layers
  • Exponential Layers
  • Shishkin Meshes
  • Local-Projection
  • Higher Order Fem

Abstract

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 ε-uniform convergence of order p for the Galerkin FEM and the LPSFEM for a singularly perturbed convection–diffusion problem with characteristic boundary layers.

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