Full Discretization of the Porous Medium/fast Diffusion Equation Based on Its Very Weak Formulation
نویسنده
چکیده
Abstract. The very weak formulation of the porous medium/fast diffusion equation yields an evolution problem in a Gelfand triple with the pivot space H. This allows to employ methods of the theory of monotone operators in order to study fully discrete approximations combining a Galerkin method (including conforming finite element methods) with the backward Euler scheme. Convergence is shown even for rough initial data and right-hand sides. The theoretical results are illustrated for the piecewise constant finite element approximation of the porous medium equation with the δ-distribution as initial value. As a byproduct, L-stability of theH-orthogonal projection onto the space of piecewise constant functions is shown.
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