HP-finite element methods for singular perturbations
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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.
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HP-finite element methods for singular perturbations, Jens M. Melenk
- Sprache
- Erscheinungsdatum
- 2002
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- Titel
- HP-finite element methods for singular perturbations
- Sprache
- Englisch
- Autor*innen
- Jens M. Melenk
- Verlag
- Springer
- Erscheinungsdatum
- 2002
- ISBN10
- 3540442014
- ISBN13
- 9783540442011
- Reihe
- Lecture notes in mathematics
- Kategorie
- Mathematik
- Beschreibung
- 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.