Hp-Finite 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: Book
Language:English
Subjects:
Analysis
Differential equations, partial
Differential equations, Partial-Numerical solutions
Engineering mathematics
Global analysis
Global analysis (Mathematics)
Global Analysis and Analysis on Manifolds
Mathematical and Computational Engineering
Mechanical engineering
Numerical analysis
Partial Differential Equations
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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.
DOI:10.1007/b84212