Volume 50, Number 4, July-August 2016
|Page(s)||1011 - 1033|
|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,
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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