A non-mortar mixed finite element method for elliptic problems on non-matching multiblock grids Original Research Article

We consider the approximation of second-order elliptic equations on domains that can be described as a union of sub-domains or blocks. We assume that a grid is defined on each block independently, so that the resulting grid over the entire domain need not be conforming (i.e. match) across the block boundaries. Several techniques have been developed to approximate elliptic equations on multiblock grids that utilize a mortar finite element space defined on the block boundary interface itself. We define a mixed finite element method that does not use such a mortar space. The method has an advantage in the case where adaptive local refinement techniques will be used, in that there is no mortar grid to refine. As is typical of mixed methods, our method is locally conservative element-by-element; it is also globally conservative across the block boundaries. Theoretical results show that the approximate solution converges at the optimal rate to the true solution. We present computational results to illustrate and confirm the theory.