A weak Galerkin finite element method for solving time-fractional coupled Burgers' equations in two dimensions

Abstract

In this paper, we present a continuous and discrete time weak Galerkin finite element method (WG-FEM) for solving two dimensional time fractional coupled Burgers' equations. The stability is proved for discrete time WG-FEM and the optimal order error in L2-norm is obtained based on fractional derivative definition, fractional integral definition and dual argument technique for continues and discrete time WG-FEM. The numerical example is to illustrate the theoretical analysis with polynomial mixture {Pk(K),Pk−1(∂K),[Pk−1(K)]2}.