Adaptive Finite Element Methods for Flows in Porous Media

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In this thesis we consider the numerical approximation of porous media flows employing finite element methods. In particular, we shall derive efficient and reliable a posteriori error bounds for the computation of certain output functionals of practical relevance. These error estimates will then be implemented within automatic adaptive mesh refinement algorithms in order to compute solutions to within a prescribed error tolerance. Finally, we shall consider the application of these techniques to problems of engineering interest, such as, for example, a problem based on the geological units found at the Sellafield site in the UK.