有限元方法: 精度及其改善

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Elsevier, 2006 - Mathematics - 320 pages
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Distributed by Elsevier Science on behalf of Science Press.

This book discusses the accuracy of various finite element approximations and how to improve them, with the help of extrapolations and super convergence's post-processing technique. The discussion is based on asymptotic expansions for finite elements and finally reduces to the technique of integration by parts, embedding theorems and norm equivalence lemmas. The book is also devoted to explaining the origin of theorems.

* Masterly exposition of the accuracy and improvement of finite element methods, highlighting the postprocessing
* Emphasis on understanding of higher knowledge
* Accessible to students, engaging for experts and professionals
* Written by leading Chinese mathematicians, available internationally for the first time
 

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Contents

Eulers Algorithm and Finite Element Method
3
Function Spaces and Norm Equivalence Lemmas
23
From K to Eigenvalue Computation of PDEs
65
Appendix 1
110
Appendix 2
120
Appendix 3
132
Appendix 4
143
First Part Bibliography
149
Expansion of Integrals on Rectangular Elements
165
Expansion of Integrals on Triangle Elements
226
Quasisuperconvergence and Quasiexpansion
252
Postprocessing
298
Second Part Bibliography
317
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