HP-infinite element methods for singular perturbations

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-co...

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Bibliographic Details
Main Author Melenk, Jens M
Format eBook
LanguageEnglish
Published Springer 15.09.2006
SeriesLecture notes in mathematics
Subjects
Differential equations, Partial
Singular perturbations (Mathematics)
Online AccessGet full text
ISBN9783540442011
3540442014

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Summary: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.
ISBN:9783540442011
3540442014