A posteriori error estimation and adaptivity for multiscale finite element approximations

• Grant number: 20/06301-6
• Support Opportunities: Scholarships in Brazil - Master
• Start date: October 01, 2020
• End date: March 31, 2022
• Field of knowledge: Engineering - Mechanical Engineering
• Agreement: Equinor (former Statoil)
• Principal Investigator: Philippe Remy Bernard Devloo
• Grantee: Gustavo Alcalá Batistela
• Host Institution: Centro de Estudos de Energia e Petróleo (CEPETRO). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Company: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Mecânica (FEM)
• 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)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BATISTELA, GUSTAVO ALCALA; DE SIQUEIRA, DENISE; DEVLOO, PHILIPPE R. B.; GOMES, SONIA M.. A posteriori error estimator for a multiscale hybrid mixed method for Darcy's flows. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, v. 123, n. 24, p. 27-pg., 2022-09-14. (17/15736-3, 20/06301-6)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

BATISTELA, Gustavo Alcalá. Estimação de erro a posteriori para o método dos elementos finitos híbrido-misto multiescala. 2023. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Civil, Arquitetura e Urbanismo Campinas, SP.