Discontinuous Galerkin Finite Element Method for Nonlinear Parabolic Problems with Non-smooth Data

Abstract:

In a recent paper \cite{KHB}, time discretization scheme was developed for discontiuous Galerkin method for a class of parabolic partial differential equations. The non-uniform time discretization is based upon the {\it a priori} knowledge of the weak singularity of $\| u_t(t)\|_2$. One of the goals of this paper is to generalize the results obtained in \cite{KHB} to a class of nonlinear parabolic equations. The nonlinear system of equations is solved by two different iterative methods and the corresponding error estimate is provided.