The aim of the lecture is to give an introduction to a very active field of research in numerical analysis. The lecture may yield a basis for a bachelor or diploma thesis which can also be written in the frame of a current research project at Institute for Analysis and Scientific Computing.
Accurate a posteriori error estimation plays a key role in reliable and efficient scienti c computing: First, one may want to check whether the solution of a numerical simulation is accurate enough. The accuracy of numerical approximations to solutions of PDEs, however, usually suffers from singularities and anisotropies of the given data and/or the (unknown) exact solution. Second, if the approximation is thus not suciently accurate, one remedy is to use meshes which resolve these singularities appropriately. Such meshes are usually obtained iteratively by adaptive algorithms which are driven by certain a posteriori error estimators.
The ultimate goal of adaptive mesh-re fining schemes is to compute a discrete solution with error below a prescribed tolerance at the expense of, up to a multiplicative constant, the minimal computational cost. In recent years, the mathematical understanding of this ultimate goal has matured. The lecture aims to give an overview on the current state of research. Interested participants can join our group and contribute to recent research activities.
The hand written lecture preparations can be downloaded from the lecture's homepage. Lecture notes will (hopefully) be written during the term.
oral examination
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