hp-Finite Element Methods for Singular Perturbations

• Main Author: Melenk, Jens M. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Edition: 1st ed. 2002.
• Series: Lecture Notes in Mathematics, 1796
• Subjects: Mathematical analysis.; Analysis (Mathematics).; Applied mathematics.; Engineering mathematics.; Mechanical engineering.; Numerical analysis.; Global analysis (Mathematics).; Manifolds (Mathematics).; Partial differential equations.; Analysis.; Mathematical and Computational Engineering.; Mechanical Engineering.; Numerical Analysis.; Global Analysis and Analysis on Manifolds.; Partial Differential Equations.
• Physical Description: XIV, 326 p. online resource.
• ISBN: 9783540457817
• ISSN: 0075-8434 ;
• DOI: 10.1007/b84212

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.