In collaboration with J.E. Pasciak and P.S. Vassilevski.
The mortar method for coupling/decomposing various approximation techniques has become an important tool in the analysis and construction of discretization schemes for multidimensional problem on non-matching grids.
In the talk we shall first introduce on a differential level two hybrid formulations, which are bases for the mortar and non-mortar approximations of second order elliptic equations on non-matching grids. Next, we shall discuss the mortar finite volume element and mortar mixed finite element discretizations and shall outline the main steps in the stability and error analysis.
Finally, we shall present some numerical experiments on model second order problems arising in ground-water simulations while applying adaptive local grid refinement.
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