An algorithm for one-dimensional Generalized Porous Medium Equations: interface tracking and the hole filling problem
Léonard Monsaingeon · arXiv (Cornell University) · 2014
Based on results of E. DiBenedetto and D. Hoff we propose an explicit finite difference scheme for the one dimensional Generalized Porous Medium Equation $\partial_t u=\partial_{xx}^2 Φ(u)$. The scheme allows to track the moving free boundaries and captures the hole filling phenomenon when two free boundaries collide. We give an abstract convergence result when the mesh parameter $Δx\to 0 $ without any error estimates, and invesigate numerically the convergence rates.