An algorithm for one-dimensional Generalized Porous Medium Equations: interface tracking and the hole filling problem

Leonard Monsaingeon

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arXiv · 1410.1473

An algorithm for one-dimensional Generalized Porous Medium Equations: interface tracking and the hole filling problem

Leonard Monsaingeon

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Abstract

Based on results of E. DiBenedetto and D. Hoff we propose an explicit finite difference scheme for the one dimensional Generalized Porous Medium Equation $\partial_t u=\partial_{xx}^2 \Phi(u)$. 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 $\Delta x\to 0 $ without any error estimates, and invesigate numerically the convergence rates.

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Leonard Monsaingeon. 2014-10-06. An algorithm for one-dimensional Generalized Porous Medium Equations: interface tracking and the hole filling problem. https://arxiv.org/abs/1410.1473

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