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

摘要

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.