hp-Finite Element Methods for Singular Perturbations
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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.
Includes supplementary material: sn.pub/extras
Autor*in
Jens M. Melenk
Themen in »hp-Finite Element Methods for Singular Perturbations«
FEM design elliptic regularity finite element method fluid mechanics high order method modeling non-smooth domains singular perturbation spectral method partial differential equations