有限元方法: 精度及其改善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 postprocessing 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.

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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 
Common terms and phrases
adjacent elements ah(u BH lemma bilinear interpolation boundary brokenline common edge Consider the functional construct postprocessing interpolation convergence defined derivatives direct computation shows domain dxdy ECHL edgeintegral eigenfunction EQ\ot error estimate error expansion Example expansion lemma extrapolation finite difference method finite element interpolation finite element method finite element solution finite element space fishbone four small elements function space fundamental formula G Vh give a proof gives the lemma Green formula h2 f Hq(Q interpolation function inverse inequality isosceles right triangle L2norm Legendre polynomial Lin Q line integrals mixed element space nonconforming elements nonconforming error norm equivalence lemma piecewise Poisson equation polygon polynomial Proof Let prove quasisuperconvergence Ratio(2 real superconvergence reference element right triangle mesh rotated bilinear element satisfies scaling argument gives Schwartz inequality Sobolev embedding theorem Suppose that Vh uniform convergence uniform rectangular mesh vector vertices Vh,o weak equation wxvxdxdy zero