Superconvergence in Galerkin Finite Element Methods

Lars B. Wahlbin (auth.)3540600116, 9783540600114

This book is essentially a set of lecture notes from a graduate seminar given at Cornell in Spring 1994. It treats basic mathematical theory for superconvergence in the context of second order elliptic problems. It is aimed at graduate students and researchers. The necessary technical tools are developed in the text although sometimes long proofs are merely referenced.
The book gives a rather complete overview of the field of superconvergence (in time-independent problems). It is the first text with such a scope. It includes a very complete and up-to-date list of references.

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Table of contents :
Some one-dimensional superconvergence results….Pages 1-27
Remarks about some of the tools used in Chapter 1….Pages 28-35
Local and global properties of L 2 -projections….Pages 36-41
Introduction to several space dimensions: some results about superconvergence in L 2 -projections….Pages 42-47
Second order elliptic boundary value problems in any number of space dimensions: preliminary considerations on local and global estimates and presentation of the main technical tools for showing superconvergence….Pages 48-64
Superconvergence in tensor-product elements….Pages 65-73
Superconvergence by local symmetry….Pages 74-83
Superconvergence for difference quotients on translation invariant meshes….Pages 84-92
On superconvergence in nonlinear problems….Pages 93-97
Chapter 10. Superconvergence in isoparametric mappings of translation invariant meshes: an example….Pages 98-106
Superconvergence by averaging: mainly, the K -operator….Pages 107-124
A computational investigation of superconvergence for first derivatives in the plane….Pages 125-135