有限元超收斂分析及后驗誤差估計

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 notes
Chapter 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 identities
Chapter 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 equations
Chapter 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 examples
Chapter 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 examples
Bibliography