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Superconvergence in Galerkin Finite Element Methods

  • Book
  • © 1995

Overview

Authors:
  1. Lars B. Wahlbin
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1605)

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About this book

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.

Keywords

Table of contents (12 chapters)

  1. Front Matter

    Pages i-xi
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  2. Some one-dimensional superconvergence results

    • Lars B. Wahlbin
    Pages 1-27

  3. Remarks about some of the tools used in Chapter 1

    • Lars B. Wahlbin
    Pages 28-35

  4. Local and global properties of L 2-projections

    • Lars B. Wahlbin
    Pages 36-41

  5. Introduction to several space dimensions: some results about superconvergence in L 2-projections

    • Lars B. Wahlbin
    Pages 42-47

  6. 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

    • Lars B. Wahlbin
    Pages 48-64

  7. Superconvergence in tensor-product elements

    • Lars B. Wahlbin
    Pages 65-73

  8. Superconvergence by local symmetry

    • Lars B. Wahlbin
    Pages 74-83

  9. Superconvergence for difference quotients on translation invariant meshes

    • Lars B. Wahlbin
    Pages 84-92

  10. On superconvergence in nonlinear problems

    • Lars B. Wahlbin
    Pages 93-97

  11. Superconvergence in isoparametric mappings of translation invariant meshes: an example

    • Lars B. Wahlbin
    Pages 98-106

  12. Superconvergence by averaging: mainly, the K-operator

    • Lars B. Wahlbin
    Pages 107-124

  13. A computational investigation of superconvergence for first derivatives in the plane

    • Lars B. Wahlbin
    Pages 125-135

  14. Back Matter

    Pages 136-168
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Bibliographic Information

  • Book Title: Superconvergence in Galerkin Finite Element Methods

  • Authors: Lars B. Wahlbin

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0096835

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1995

  • Softcover ISBN: 978-3-540-60011-4Published: 14 July 1995

  • eBook ISBN: 978-3-540-49401-0Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 172

  • Topics: Numerical Analysis, Analysis

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