This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. It formalizes basic tools that are commonly used by researchers in the field but not previously published. The book will be useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory.

Klappentext

A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as many new exercises; Previous edition sold over 3000 copies worldwide

Inhalt

Preface(2ndEd)Preface(1stED)Basic ConceptsSobolev SpacesVariational Formulation of Elliptic Boundary Value ProblemsThe Construction of a Finite Element of SpacePolynomial Approximation Theory in Sobolev Spacesn-Dimensional Variational ProblemsFinite Element Multigrid MethodsAdditive Schwarz PreconditionersMax-norm EstimatesAdaptive MeshesVariational CrimesApplications to Planar ElasticityMixed MethodsIterative Techniques for Mixed MethodsApplications of Operator-Interpolation TheoryReferencesIndex