Abstract: We solved timedependent Brinkman equation by the weak Galerkin finite element method. Corresponding error equations and error estimates were established by using semidiscrete scheme only for the discrete space and fulldiscrete scheme for the time and space discretization. We obtained the optimal rate convergence in H¹ and L² norm for the velocity function, and in H¹ norm for the pressure function. So that the weak Galerkin finite element method was applied more widely.

Key words: weak Galerkin finite element method, vector discrete weak gradient, scalar discrete weak gradient, timedependent Brinkman equation