B2

Long Chen and Jinchao Xu. Topics on Adaptive Finite Element Methods.

CONTENT:

1 Convergence of Adaptive Finite Element Methods 2
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Residual type error estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 Convergence of an adaptive finite element method . . . . . . . . . . . . . . . . 19
1.5 Optimality of the adaptive finite element method . . . . . . . . . . . . . . . . 24

1 A Posteriori Error Estimator by Post-processing 2
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Linear finite element on patch symmetric grids . . . . . . . . . . . . . . . . . 6
1.3 Linear finite element on mildly structured grids . . . . . . . . . . . . . . . . . 11
1.4 Linear finite element on general unstructured grids . . . . . . . . . . . . . . . 18