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A posteriori error indicators and adaptive refinement

Adaptive refinement strategies based on a posteriori error estimators form one of the basic tools to obtain efficient and reliable algorithms for the numerical approximation of partial differential equations. One of the main ideas is to equilibrate the local error during the refinement process and to refine the triangulation in critical regions where the solution is less regular. Very often, the adaptive refinement process is controlled by locally defined a posteriori error estimators which provide upper and lower bounds for the error. There is a large variety of different types of error estimators such as: residual based and hierarchical ones and error estimators based on the solution of local subproblems, averaging techniques or dual methods.

Introduction to adaptive refinement methods (PDF in German)