Regularity Of The Solutions For Elliptic Problems On Nonsmooth Domains In R3 Part 2 Regularity In Neighborhoods Of Edges
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Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012
Author: Mejdi Azaïez
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-11-19
The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2012), and provides an overview of the depth and breath of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.
Regularity of the Solutions for Elliptic Problems on Nonsmooth Domains in R3. Part 2: Regularity in Neighborhoods of Edges
This paper is the second in a series of three devoted to the analysis of regularity of solutions of elliptic problems on nonsmooth domains in R3. The present paper concentrates on the regularity of solution of Poisson equation in neighborhoods of edges of a polyhedral domain in the frame of the weighted Sobolev spaces and countably normed spaces. These results can be generalized to elliptic problems arising form mechanics and engineering; for instance, the elasticity problem on polyhedral domains.
Graded Finite Element Methods for Elliptic Problems in Nonsmooth Domains
This book develops a class of graded finite element methods to solve singular elliptic boundary value problems in two- and three-dimensional domains. It provides an approachable and self-contained presentation of the topic, including both the mathematical theory and numerical tools necessary to address the major challenges imposed by the singular solution. Moreover, by focusing upon second-order equations with constant coefficients, it manages to derive explicit results that are accessible to the broader computation community. Although written with mathematics graduate students and researchers in mind, this book is also relevant to applied and computational mathematicians, scientists, and engineers in numerical methods who may encounter singular problems.