Mortar methods for approximation of macroscopic conductivity
نویسندگان
چکیده
Mortar method is proposed to form a macroscopic model for a problem with a multiscale conductivity. The macroscopic model is built on the coarse uniform grid quipped for the problem domain. For each uniform grid, artificial neighboring cells are attached to form a model which includes the localized microscale model. For the proposed model, a very fine mesh is introduced to resolve the microscale conductivity while a uniform coarse mesh is introduced for the artificial neighboring cells, where the conductivity is given as a uniform value one. The resulting mesh is thus nonmatching across the cell interfaces and mortar methods are used to form a discrete problem for the model. After finding the discrete solution, an approximation of the macroscopic conductivity is obtained by solving a nonlinear minimization problem. Numerical experiments are carried out to show a promising feature of the proposed method for random and high contrast coefficients compared to the existing homogenization approaches.
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