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
