Weak Galerkin Finite Element Methods for Parabolic Interface Problems with Nonhomogeneous Jump Conditions

The numerical solution of a second- order linear parabolic interface problem by weak Galerkin finite element method is discussed. This method allows the usage of totally discontinuous functions in approximation space and preserves the energy conservation law. In the implementation, the weak partial derivatives and the weak functions are approximated by polynomials with various degrees of freedom. The accuracy and the computational complexity of the corresponding WG scheme is significantly impacted by the selection of such polynomials. This paper presents an optimal combination for the polynomial spaces that minimize the number of unknowns in the numerical scheme without compromising the accuracy of the numerical approximation. More precisely, optimal order error estimates in both H-1 and L-2 norms are established for lowest order WG finite element space (P-k(K); (Pk-1(partial derivative K), [Pk-1(K)](2)). Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polygonal meshes.