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

In: Mathematics — Key Technology for the Future

Author

Listed:
  • 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.)

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.

Suggested Citation

  • Jürgen Fuhrmann & Martin Petzoldt, 2003. "Robust Error Estimators for Interface Problems Occuring in Transport Processes in Porous Media," Springer Books, in: Willi Jäger & Hans-Joachim Krebs (ed.), Mathematics — Key Technology for the Future, pages 127-136, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55753-8_10
    DOI: 10.1007/978-3-642-55753-8_10
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