Superconvergence in Galerkin Finite Element Methods

by Lars Wahlbin

Overview

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.

Product Details

ISBN-13:	9783540600114
Publisher:	Springer Berlin Heidelberg
Publication date:	08/25/1995
Series:	Lecture Notes in Mathematics , #1605
Edition description:	1995
Pages:	172
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

Some one-dimensional superconvergence results.- Remarks about some of the tools used in Chapter 1.- Local and global properties of L 2-projections.- to several space dimensions: some results about superconvergence in L 2-projections.- 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.- Superconvergence in tensor-product elements.- Superconvergence by local symmetry.- Superconvergence for difference quotients on translation invariant meshes.- On superconvergence in nonlinear problems.- 10. Superconvergence in isoparametric mappings of translation invariant meshes: an example.- Superconvergence by averaging: mainly, the K-operator.- A computational investigation of superconvergence for first derivatives in the plane.