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) of index one. A priori 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.
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