有限元超收斂分析及后驗(yàn)誤差估計(jì)

內(nèi)容概要

　　Since the 1970s,Science press has published more than thirty volumes in its series Monographs in Computational Methods. This series was established and led by the late academician,Feng Kang,the founding director for Computing Center of the Chinese Academy of Sciences.The monograph series has provided timely information of the frontier directions and latest research results in computational mathematics.It has had great impact on young scientists and the entire research community,and has played a very important role in the development of computational mathematics in China.

書籍目錄

Chapter 1 Basic framework　1.1　Preliminaries　1.2　Model problem　1.3　Integral identity　1.4　Global superconvergence analysis　1.5　Brief summary and notesChapter 2 Integral identities　2.1　Bilinear rectangular element　2.2　General results for bilinear element　2.3　Rectangular Lagrange elements of order p　2.4　Rectangular finite elements with derivative degrees of freedom　2.5　Rectangular mixed finite elements　2.6　Summary of integral identitiesChapter 3  Superconvergenee Analysis　3.1  Elliptic partial differential equations　3.2  Nonconforming finite elements　3.3  Evolution partial differential equationss　3.4  Hyperbolic equation of order one　3.5  Mixed finite elements　3.6  Integral equationsChapter 4  More discussions on high accuracy analysis　4.1  Global superconvergence　4.2  Extrapolation　4.3  Defect correction　4.4  Local superconvergence　4.5  Ultraconvergence　4.6  Eigenvalue problems　4.7  Numerical examplesChapter 5  A posteriori error estimates　5.1  Introduction　5.2  Residual type a posteriori error estimate　5.3  Recovery type a posteriori error estimate　5.4  Equivalence of recovery type estimator　5.5  Asymptotically exactness of recovery type estimator　5.6  Some remarks on two kinds of estimators　5.7  A posteriori error estimate for optimal control problems 　5.8  Numerical examplesBibliography

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