| Issue |
ESAIM: M2AN
Volume 50, Number 4, July-August 2016
|
|
|---|---|---|
| Page(s) | 1011 - 1033 | |
| DOI | https://doi.org/10.1051/m2an/2015063 | |
| Published online | 16 June 2016 | |
An explicit finite-difference scheme for one-dimensional Generalized Porous Medium Equations: Interface tracking and the hole filling problem
CAMGSD, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa,
Portugal.
leonard.monsaingeon@ist.utl.pt
Received:
6
April
2015
Revised:
11
July
2015
Based on results of E. DiBenedetto and D. Hoff we propose an explicit finite-difference scheme for one dimensional Generalized Porous Medium Equations ∂tu = ∂xx2 Φ(u). The scheme allows to track the moving free boundaries, and captures the so-called hole filling phenomenon when free boundaries collide. We prove the convergence of the discrete solution when the mesh parameter Δx → 0. Finally, we provide numerical evidence of the convergence of the scheme.
Mathematics Subject Classification: 65M06 / 35R35 / 35K65
Key words: Generalized porous medium equation / interface tracking / hole filling / finite-difference
© EDP Sciences, SMAI 2016
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