Session S20 - Applied Math and Computational Methods and Analysis across the Americas

Friday, July 16, 18:30 ~ 19:00 UTC-3

The MHM method for Linear Elasticity

Weslley da Silva Pereira

Laboratório Nacional de Computação Científica, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The multiscale hybrid-mixed (MHM) method consists of a multi-level strategy to approximate the solution of boundary value problems with heterogeneous coefficients. One may find in the literature a couple of families of finite elements that can be used for the MHM methods in the context of linear elasticity. These finite elements rely on face degrees of freedom associated with a basis that is obtained from the solution of local Neumann elasticity problems. The local problems are independent of one another, and can therefore be solved in parallel trivially. Heterogeneities present in both the physical coefficients and source are considered at the finest-scale level, and the bases associated with the face degrees of freedom are responsible for bringing this information to the coarsest scale solution. In this talk, we present the MHM method for linear elasticity and some of its finite elements defined on coarse polytopal partitions. We show recent results on stability and convergence that mainly depend on local regularity assumptions. In particular, the multi-level error analysis demonstrates that the MHM method achieves convergence without changing the coarse partition. We show some numerical tests that assess theoretical results and verify the robustness of the method.

Joint work with Antônio Tadeu Gomes (Laboratório Nacional de Computação Científica, Brazil) and Frédéric Valentin (Laboratório Nacional de Computação Científica, Brazil).

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