Optimal error estimates for an approximation of degenerate parabolic equations with time-dependent operators

Abstract This paper presents an abstract framework for the analysis of a numerical scheme designed for degenerate parabolic equations with time-dependent operators. We derive quasi-optimal error estimates for the approximation and establish sufficient conditions that guarantee the existence of a unique numerical solution. In our analysis, we use a finite element method for the spatial discretization and an implicit Euler scheme for the temporal discretization. Furthermore, applications with different operator choices are considered to illustrate the abstract theory. Finally, numerical experiments are carried out in order to validate the performance of the method and to corroborate our theoretical results.