Graded Finite Element Methods for Elliptic Problems in Nonsmooth Domains
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Beschreibung
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.
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.
Suitable for researchers as well as graduate and postdoc students Uniquely presents both theory and numerical algorithms for singularities Focuses on refining techniques with cross-disciplinary applications
Autor*in
Hengguang Li
Themen in »Graded Finite Element Methods for Elliptic Problems in Nonsmooth Domains«
graded finite element method anisotropic mesh algorithm elliptic boundary value problem nonsmooth domain singular solution regularity analysis weighted Sobolev space optimal convergence mixed boundary condition