Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux
Numerical Analysis
2008-07-03 v1 Analysis of PDEs
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 Engquist--Osher approximation for the flux and explicit time--stepping. An adaptivemultiresolution scheme with cell averages is then used to speed up CPU time and meet memory requirements. A particular feature of our scheme is the storage of the multiresolution representation of the solution in a dynamic graded tree, for the 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.
Keywords
Cite
@article{arxiv.0807.0403,
title = {Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux},
author = {Raimund Bürger and Ricardo Ruiz Baier and Mauricio Sepúlveda and Kai Schneider},
journal= {arXiv preprint arXiv:0807.0403},
year = {2008}
}