Numerische Simulation Auf Massiv Parallelen Rechnern Error Estimation for Anisotropic Tetrahedral and Triangular Nite Element Meshes

Some boundary value problems yield anisotropic solutions, e.g. solutions with boundary layers. If such problems are to be solved with the nite element method (FEM), anisotropically reened meshes can be advantageous. In order to construct these meshes or to control the error one aims at reliable error estimators. For isotropic meshes many estimators are known, but they either fail when used on anisotropic meshes, or they were not applied yet. For rectangular (or cuboidal) anisotropic meshes a modiied error estimator had already been found. We are investigating error estimators on anisotropic tetrahedral or triangular meshes because such grids ooer greater geometrical exibility. For the Poisson equation a residual error estimator, a local Dirichlet problem error estimator, and an L 2 error estimator are derived, respectively. Additionally a residual error estimator is presented for a singularly perturbed reaction diiusion equation. It is important that the anisotropic mesh corresponds to the anisotropic solution. Provided that a certain condition is satissed, we have proven that all estimators bound the error reliably.