Numerical Methods for Elliptic Problems with Singularities: Boundary Methods and Nonconforming Combinations

Description

This book presents two kinds of numerical methods for solving elliptic boundary value problems with singularities. Part I gives the boundary methods which use analytic and singular expansions, and Part II the nonconforming methods combining finite element methods (FEM) (or finite difference methods (FDM)) and singular (or analytic) expansions. The advantage of these methods over the standard FEM and FDM is that they can cope with complicated geometrical boundaries and boundary conditions as well as singularity. Therefore, accurate numerical solutions near singularities can be obtained. The description of methods, error bounds, stability analysis and numerical experiments are provided for the typical problems with angular, interface and infinity singularities. However, the approximate techniques and coupling strategy given can be applied to solving other PDE and engineering problems with singularities as well. This book is derived from the author's Ph. D. thesis which won the 1987 best doctoral dissertation award given by the Canadian Applied Mathematics Society. Contents:IntroductionPart I:Boundary Methods for Solving Laplace's Boundary Value Problems with SingularitiesA Complicated Problem Solved by Boundary MethodsBoundary Methods for Interface ProblemsPart II:The Nonconforming Combination of the Ritz-Galerkin and Finite Element MethodsThe Nonforming Combinations for Infinite Domain ProblemsThe Nonconforming Combinations for Interface ProblemsThe Nonconforming Combination of the Ritz-Galerkin and Finite Difference MethodsReferences, Index Readership: Computer scientists, applied mathematicians and engineers. Keywords:Elliptic Problems;Finite Element Method;Finite Difference Method;Ritz-Galerkin Method;Boundary Element Method;Least Squares Method;Singularity Problems;Boundary Methods;Nonconforming Combinations

Get the book

Amazon.com

Search the book

eBay.com

Search the book