Higher order fully discrete scheme combined with H¹-Galerkin mixed finite element method for semilinear reaction-diffusion equations

Abstract

We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by an H¹-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) ofindex one. Apriori error estimates for semidiscrete scheme are derived for both differential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example.