Numerische Simulation Auf Massiv Parallelen Rechnern Anisotropic Mesh Reenement for Singularly Perturbed Reaction Diiusion Problems
نویسندگان
چکیده
The paper is concerned with the nite element resolution of layers appearing in singularly perturbed problems. A special anisotropic grid of Shishkin type is constructed for reaction diiusion problems. Estimates of the nite element error in the energy norm are derived for two methods, namely the standard Galerkin method and a stabilized Galerkin method. The estimates are uniformly valid with respect to the (small) diiusion parameter. One ingredient is a pointwise description of derivatives of the continuous solution. A numerical example supports the result. Another key ingredient for the error analysis is a reened estimate for (higher) derivatives of the interpolation error. The assumptions on admissible anisotropic nite elements are formulated in terms of geometrical conditions for triangles and tetrahedra. The application of these estimates is not restricted to the special problem considered in this paper.
منابع مشابه
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 a...
متن کاملNumerische Simulation auf massiv parallelen Rechnern
The paper deals with a singularly perturbed reaction diffusion model problem. The focus is on reliable a posteriori error estimators for the H1 seminorm that can be applied to anisotropic finite element meshes. A residual error estimator and a local problem error estimator are proposed and rigorously analysed. They are locally equivalent, and both bound the error reliably. Furthermore three mod...
متن کاملNumerische Simulation Auf Massiv Parallelen Rechnern Domain Decomposition for Isotropic and Anisotropic Elliptic Problems Preprint-reihe Des Chemnitzer Sfb 393
متن کامل
Numerische Simulation Auf Massiv Parallelen Rechnern Stability of Discretizations of the Stokes Problem on Anisotropic Meshes
Abstract Anisotropic features of the solution of ow problems are usually approximated on anisotropic (large aspect ratio) meshes. This paper reviews stability results of several velocity-pressure pairs with respect to growing aspect ratio of the elements in the mesh. For further pairs numerical tests are described. Related results are mentioned.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996