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A multiscale mortar mixed space based on homogenization for heterogeneous elliptic problems. (English) Zbl 1267.65192

The authors are concerned with the classic linear second-order elliptic equation with a heterogeneous coefficient in a domain decomposition setting and in a mixed form. They take into account the effect of a fine scale on the solution (the pair, velocity and convergence) and define a new mortar space of functions. In this space, the pressure on each interface of subdomains is approximated using the homogenization theory. The introduced mortar space is based on polynomials, but it is itself nonpolynomial. A thorough convergence analysis and three numerical tests are carried out. They emphasize nonperiodic permeability fields. By these numerical examples the authors show that their mortar space performs better than purely polynomial-based mortar spaces.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65Y05 Parallel numerical computation

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