Superconvergence in Galerkin Finite Element Methods

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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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.

• Boundary value problem
• boundary element method
• convergence
• derivative
• finite element method

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