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

摘要

For a general class of finite element spaces based on local polynomial spaces ε with ρ_pCεCQ_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.