
| 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 |
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