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内容简介
《椭圆方程有限元方法的整体超收敛及其应用(英文版)》内容简介：This book covers the advanced study on the global superconvegence of elliptic equations in both theory and computation,where the main materials are adapted from our journal papers published.A deep and rather completed analysis of global supperconvergence is explored for bilinear,biquadratic,Adini”s and bi-cubic Hermite elements,as well as for the finite difference method.Poisson”s and the biharmonic equations are included,and eigenvalue and semi-linear problems are discussed.The singularity problems,blending problems,coupling techniques,a posteriori interpolant techniques,and some physical and engineering problems are studied.Numerical examples are proviede for verification of the analysis,and other numerical experiments can be found from our publications.This book has also summarized some important results of Lin,his colleagues and others.This book is written for researchers and graduate students of mathematics and engineering to study and apply the global superconvergence for numerical PDE.
目 录
PrefaceAcknowledgementsChapter 1 Basic Approaches1.1 Introduction1.2 Simplified Hybrid Combined Methods1.3 Basic Theorem for Global Superconvergence1.4 Bilinear Elements1.5 Numerical Experiments1.6 Concluding RemarksChapter 2 Adini”s Elements2.1 Introduction2.2 Adini”s Elements2.3 Global Superconvergence2.3.1 New error estimates2.3.2 A posteriori interpolant formulas2.4 Proof of Theorem 2.3.12.4.1 Preliminary lemmas2.4.2 Main proof of Theorem 2.3.12.5 Stability Analysis2.6 New Stability Analysis via Effective Condition Number2.6.1 Computational formulas2.6.2 Bounds of effective condition number2.7 Numerical Experiments and Concluding RemarksChapter 3 Biquadratic Lagrange Elements3.1 Introduction3.2 Biquadratic Lagrange Elements3.3 Global Superconvergence3.3.1 New error estimates3.3.2 Proof of Theorem 3.3.13.3.3 Proof of Theorem 3.3.23.3.4 Error bounds for Q8 elements3.4 Numerical Experiments and Discussions3.4.1 Global superconvergence3.4.2 Special case of h=k and fxxyy=03.4.3 Comparisons3.4.4 Relation between uh and ū*h3.5 Concluding RemarksChapter 4 Simplified Hybrid Method for Motz”s Problems4.1 Introduction4.2 Simplified Hybrid Combined Methods4.3 Lagrange Rectangular Elements4.4 Adini”s Elements4.5 Concluding RemarksChapter 5 Finite Difference Methods for Singularity Problems5.1 Introduction5.2 The Shortley-Weller Difference Approximation5.3 Analysis for uDh with no Error of Divergence Integration5.4 Analysis for uh with Approximation of Divergence Integration5.5 Numerical Verification on Reduced Convergence Rates5.5.1 The model on stripe domains5.5.2 The Richardson extrapolation and the least squares method5.6 Concluding RemarksChapter 6 Basic Error Estimates for Biharmonic Equations6.1 Introduction6.2 Basic Estimates for ∫∫Ω(u-uI)xxvxxds6.3 Basic Estimates for ∫∫Ω(u-uI)xyvxyds6.4 New Estimates for ∫∫Ω(u-uI)xyvxyds for Uniform Rectangular Elements6.5 New Estimates for ∫∫Ω(u-uI)xxvyyds6.6 Main Theore……
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