Adaptive Finite Element Methods for Flows in Porous Media

在本论文中，我们考虑了用有限元方法对多孔介质流动进行数值逼近。特别是，我们将为某些具有实际意义的输出泛函的计算推导出有效和可靠的后验误差界。然后，这些误差估计将在自动自适应网格精化算法中实现，以便计算出在规定误差容限内的解。最后，我们将考虑将这些技术应用于具有工程意义的问题，例如，基于在英国Sellafield遗址发现的地质单位的问题。

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.