A Short Note On Solving 1-D Porous Medium Equation by Finite Element Methods

Abstract

Porous Medium Equation (PME) is one of the simplest types of of nonlinear evolution equation of parabolic type. It emerges in the description of different natural phenomena, and its theory and properties depart strongly from the heat equation, ut = u, its most famous relative. Hence the interest of its study, both for the pure mathematician and the applied scientist (Vazquez, 2006). The aim of this paper is to study the Porous Medium Equation in one dimension.