Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.Section 1.4.1 is concerned with regularity theory of elliptic problems on non- smooth domains. The classical theory discussed in that area does not address the issue of singular perturbation problems. Section 1.4.2 presents the approach ofanbsp;...
|Title||:||Hp-Finite Element Methods for Singular Perturbations|
|Author||:||Jens M. Melenk|
|Publisher||:||Springer Science & Business Media - 2002-10-10|