Approximation of a nonlinear degenerate parabolic equation via a linear relaxation scheme

Abstract

We study a nonlinear degenerate parabolic equation of the typeaccompanied by an initial datum and mixed boundary conditions. The symbol [ ⅐ ] ϩ denotes the usual cutoff function. The problem represents a model of a reactive solute transport in porous media. The exponent p fulfills p ʦ (0, 1). This limits the regularity of a solution and leads to inconveniences in the error analysis. We design a new robust linear numerical scheme for the time discretization. This is based on a suitable combination of the backward Euler method and a linear relaxation scheme. We prove the convergence of relaxation iterations on each time point t i . We derive the error estimates in suitable function spaces for all values of p ʦ (0, 1).