Fully Adaptive Multiresolution Schemes for Strongly Degenerate Parabolic Equations with Discontinuous Flux

  • RAIMUND BÜRGERA, RICARDO RUIZA, KAI SCHNEIDERB
  • Published 2008

Abstract

A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the approximation of Engquist-Osher for the flux and explicit time stepping. An adaptive multiresolution scheme with cell averages is then used to speed up CPU time and memory requirements. A particular feature of our scheme is the storage of the multiresolution representation of the solution in a dynamic graded tree, for sake of data compression and to facilitate navigation. Applications to traffic flow with driver reaction and a clarifier-thickener model illustrate the efficiency of this method.

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Cite this paper

@inproceedings{BRGERA2008FullyAM, title={Fully Adaptive Multiresolution Schemes for Strongly Degenerate Parabolic Equations with Discontinuous Flux}, author={RAIMUND B{\"{U}RGERA and RICARDO RUIZA and KAI SCHNEIDERB}, year={2008} }