A Multiscale Mortar Mixed Space Based on Homogenization for Heterogeneous Elliptic Problems

We consider a second order elliptic problem with a heterogeneous coefficient written in mixed form. The nonoverlapping mortar domain decomposition method is efficient in parallel if the mortar interface coupling space has a restricted number of degrees of freedom. In the heterogeneous case, we define a new multiscale mortar space that incorporates purely local information from homogenization theory to better approximate the solution along the interfaces with just a few degrees of freedom. In the case of a locally periodic heterogeneous coefficient of period ε, we prove that the new method achieves both optimal order error estimates in the discretization parameters and good approximation when ε is small. Moreover, we present three numerical examples to assess its performance when the coefficient is not obviously locally periodic. We show that the new mortar method works well, and better than polynomial mortar spaces.