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
HP-Finite Element Methods for Singular Perturbations
β Scribed by Melenk J.M.
- Year
- 2008
- Tongue
- English
- Leaves
- 340
- Category
- Library
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β¦ Synopsis
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.
π SIMILAR VOLUMES
This part of the book is devoted to the finite element approximation to solutions of A.2.11). The principal aim of the present Chapter 2 is the robust exponential convergence result Theorem 2.4.8, which is illustrated by numerical examples in Section 2.5. Essential for this robust exponential conver
Β <b>Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the Ξ΅ -uniform convergence of these schemes and surveys the latest approaches important for further progress in numerical met
Β <b>Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the Ξ΅ -uniform convergence of these schemes and surveys the latest approaches important for further progress in numerical met
<p>This book results from various lectures given in recent years. Early drafts were used for several single semester courses on singular perturbation methΒ ods given at Rensselaer, and a more complete version was used for a one year course at the Technische Universitat Wien. Some portions have been
<p>This book results from various lectures given in recent years. Early drafts were used for several single semester courses on singular perturbation methΒ ods given at Rensselaer, and a more complete version was used for a one year course at the Technische Universitat Wien. Some portions have been