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Error estimation for approximations using the multiscale hybrid mixed method

Grant number: 19/17186-6
Support type:Scholarships in Brazil - Master
Effective date (Start): October 01, 2019
Effective date (End): September 30, 2021
Field of knowledge:Engineering - Civil Engineering
Cooperation agreement: Equinor (former Statoil)
Principal Investigator:Philippe Remy Bernard Devloo
Grantee:Victor Bringhenti Oliari
Home Institution: Faculdade de Engenharia Civil, Arquitetura e Urbanismo (FEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:17/15736-3 - Engineering Research Centre in Reservoir and Production Management, AP.PCPE

Abstract

This work is a continuation of the PhD thesis of Omar Duran Triana [DURAN] who developed the computational tools to apply the Multiscale Hybrid-Mixed (MHM) [PAREDES] and Reduced Order Modeling (ROM) of geomechanic deformation [DURAN], to simulate two phase reservoir flow. The multiscale hybrid mixed allows one to simulate complex reservoir flow problems with a very reduced number of equations in the global system that needs to be inverted. This reduction in system size, although leading to physically consistent solutions, will yield a higher approximation error when compared to the full system solution (which we cannot compute due to the system size). We propose to develop an error estimator for the MHM method that allows us to evaluate which macro elements contribute to the approximation error more expressively. This will allow us to develop future adaptive strategies to adjust the multiscale discretization. As such the focus of this contribution will be: * Study existing technique to estimate the error of H(div) approximations * Extend the systematic of computing errors of H(div) to MHM computations * Compute the effectivity index of the estimated error for different configurations We recognize that the development and implementation of an error estimator is an ambitious project. However, the laboratory has a long standing experience in computing adaptive finite element approximations. Also, the student that will develop the project will be assisted by the LabMeC research team. One PhD and one master student are working on related topics. (AU)