English

On Dual-Finite Volume Methods for Extended Porous Medium Equations

Numerical Analysis 2015-07-21 v1 Numerical Analysis

Abstract

This article shows that the unconditional stability of the Dual-Finite Volume Method, which is at least valid for linear problems, is not true for generic nonlinear differential equations including the PMEs unless the coefficient appearing in the numerical fluxes are appropriately evaluated. This article provides a theoretically truly isotone numerical fluxes specialized for solving the PMEs presented, which is still as simple as the conventional fully-upwind counterpart.

Keywords

Cite

@article{arxiv.1507.05281,
  title  = {On Dual-Finite Volume Methods for Extended Porous Medium Equations},
  author = {Hidekazu Yoshioka},
  journal= {arXiv preprint arXiv:1507.05281},
  year   = {2015}
}