Geodesic
An explicit finite-difference scheme for one-dimensional Generalized Porous Medium Equations: Interface tracking and the hole filling problem
Monsaingeon, Léonard1 
1 CAMGSD, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 1011-1033

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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 Δx→0. Finally, we provide numerical evidence of the convergence of the scheme.

DOI : 10.1051/m2an/2015063
Classification : 65M06, 35R35, 35K65
Keywords: 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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     title = {An explicit finite-difference scheme for one-dimensional {Generalized} {Porous} {Medium} {Equations:} {Interface} tracking and the hole filling problem},
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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

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