Galerkin finite element methods solving 2D initial–boundary value problems of neutral delay-reaction–diffusion equations

Abstract In this paper, Galerkin finite element (GFE) methods are extended to solve two-dimensional (2D) initial–boundary value problems of neutral delay-reaction–diffusion equations, where the spatial and temporal variables are discretized by the semi-discrete GEF methods and Crank–Nicolson method, respectively. By setting some appropriate conditions, it is proved that a fully discrete GFE method is uniquely solvable, stable and convergent of order 2 in time and order r (resp. r − 1 ) in space under the sense of L 2 -norm (resp. H 1 -norm), where r − 1 ( r ≥ 2 ) denotes the degree of piecewise polynomial in finite element space. Moreover, with some numerical experiments, we further illustrate the computational effectiveness and accuracy of the method.