Weak Galerkin finite element method for linear elasticity interface problems

Abstract

In this paper, we apply a weak Galerkin finite element method to a linear elasticity interface model. Since the solution may become discontinuous while crossing the interface, we first discretize the model by double-valued weak functions on the interface. Then, in order to facilitate theoretical analysis and algorithm implementation, we substitute interface conditions into the weak Galerkin formulation and construct a weak Galerkin method with single-valued functions on the interface. Furthermore, we prove the well-posedness of the weak Galerkin scheme and derive a priori error estimates in energy norm and L2 norm. Finally, we present some numerical experiments to demonstrate the efficiency and the locking-free property of our method.