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

Monday, July 19, 17:30 ~ 18:00 UTC-3

A posteriori error estimation for a Multiscale Hybrid Mixed method

Denise de Siqueira

Federal University of Technology – Curitiba, PR, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We present a computable and efficient procedure for a posteriori error estimation for a Multiscale Hybrid Mixed method denoted by (MHM-H(div)). This is a finite element strategy for the simulation of problems with strongly varying solutions and designed to efficiently capture the solutions large-scale behavior, without considering all the small-scale features. We consider a Darcy model problem where flow normal fluxes and piecewise constant pressure approximations in each macro element are solved by a global system (upscaling). Then, small details are recovered by local Newmann problems using mixed finite elements with enriched approximation spaces (downscaling). The general methodology for the error estimation is based on potential and flux reconstruction. As the flux variable given by the method is already equilibrated only the pressure reconstruction is required. The a posteriori error estimation has two main steps: smoothing of the computed pressure variable and solving local Dirichlet problems with hybridization. The performance of the estimators is investigated through several numerical convergence tests.

Joint work with Gustavo Alcalá Batistela (University of Campinas, Brazil), Phillipe R. B. Devloo (University of Campinas, Brazil) and Sônia Maria Gomes (University of Campinas, Brazil).

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