Robust Error Estimators for Interface Problems Occuring in Transport Processes in Porous Media

Jürgen Fuhrmann and Martin Petzoldt
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Jürgen Fuhrmann: Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V.
Martin Petzoldt: Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V.

A chapter in Mathematics — Key Technology for the Future, 2003, pp 127-136 from Springer

Abstract: Abstract The aim of the project is the adptive numerical simulation of transport processes in porous media within the groundwater simulation code FEFLOW [4]. These processes can be very complex and take place in highly heterogeneous media. The nature of the describing equations is such that error estimators for the full nonlinear model can be defined only heuristically based on considerations on known model problems and numerical experiments. Here one could only proceed with heuristical error indicators, which give a criterion where to refine the grid to become probably more accurate. As adaptivity and error control suggest to the engineer that we really give him a measure of the error — i.e. an error estimate, in consensus with the industry partner, we disregarded the heuristical approach as much as we could and rather tried to verify both theoretically and experimentally estimators for a relevant problem class where we still are able to proceed with mathematical theory.

Keywords: Singular Point; Error Estimator; Coarse Mesh; Interface Problem; Constant Approxi (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-3-642-55753-8_10

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