Finite Element Approximation of the Fast Diffusion and the Porous Medium Equations

Abstract

1The fast diffusion equation $u_t=\Delta(|u|^{m-1}u)(0<m<1)$ and the porous medium equation $(1<m<\infty)$ are studied in a parabolic cylinder $\Omega\times (0,T)$. A fully discrete Galerkin approximation is considered using $C^0$-piecewise linear finite elements in space and the backward Euler time discretization. A priori error estimates in quasi norms and rates of convergence are proved.