Multilevel Grid Reenement for Elliptic Problems Based on a Posteriori Error Analysis

The behavior of many physical processes is greatly aaected by some of their localized physical properties. For such cases it is essential that local grid reenement techniques be applied. We present the results of implementation of four local error indicators, namely the residual based error indicator, an error indicator based on the approximation of the second derivatives, Zienkeiwicz-Zhu error indicator and a hierarchical basis error indicator. The implementation is done in the framework of multi-level reenement and the corresponding problems on the composite grid are solved in a multilevel fashion. We show that these four techniques give a good representation of the main ideas in local reenement strategies. The computational results of several test problems such as singular solutions in a L-shaped domain, and solutions with boundary layers are brieey discussed.