Abstract
We study an error analysis of the time-continuous semidiscrete scheme for nonlinear parabolic equations admitting fast-diffusion type of degeneracies. A typical example of such a differential equation is Richards' equation, widely used to model the fluid flow in porous media.
The solutions to this problem usually lack regularity, and they have been studied in papers on the existence, uniqueness, and regularity of solutions to elliptic-parabolic differential equations.
Due to the nonlinear diffusion, we employ the incomplete interior penalty Galerkin (IIPG) method for spatial discretization. Since the considered problem has an extra nonlinearity, namely, in the accumulation term, special techniques for numerical analysis of the scheme are required. We use continuous mathematical induction to prove a priori error estimates in the $L^2$-norm and the so-called DG-norm with respect to spatial discretization parameter and the H{\"o}lder coefficient of the accumulation term derivative.