An explicit finite-difference scheme for one-dimensional Generalized Porous Medium Equations: Interface tracking and the hole filling problem
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 1011-1033.

Based on results of E. DiBenedetto and D. Hoff we propose an explicit finite-difference scheme for one dimensional Generalized Porous Medium Equations t u = x x 2 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 Δx0. Finally, we provide numerical evidence of the convergence of the scheme.

DOI : 10.1051/m2an/2015063
Classification : 65M06, 35R35, 35K65
Mots clés : Generalized porous medium equation, interface tracking, hole filling, finite-difference
Monsaingeon, Léonard 1

1 CAMGSD, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal.
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Monsaingeon, Léonard. An explicit finite-difference scheme for one-dimensional Generalized Porous Medium Equations: Interface tracking and the hole filling problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 1011-1033. doi : 10.1051/m2an/2015063. http://www.numdam.org/articles/10.1051/m2an/2015063/

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