Mixed-Hybrid Finite Element Methods for Elliptic Problems with application to Porous Media Flow and Linear Elasticity

• Grant number: 17/23338-8
• Support Opportunities: Regular Research Grants
• Start date: March 01, 2018
• End date: February 29, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Maicon Ribeiro Correa
• Grantee: Maicon Ribeiro Correa
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This Research Project in Numerical Analysis, deals with the development of numerical methods for solving the systems of Partial Differential Equations that model the elliptic problems of single phase flow in porous media and deformation of a linear elastic body. More specifically, we propose the development and the analysis of new mixed-hybrid finite element methods to compute Darcy's velocity and pressure in highly heterogeneous rigid porous media and the pair stress-displacement in linearly elastic isotropic media. (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)

CORREA, MAICON R.; MURAD, MARCIO A.. A new sequential method for three-phase immiscible flow in poroelastic media. Journal of Computational Physics, v. 373, p. 493-532, NOV 15 2018. (17/23338-8)

CORREA, MAICON R.; RODRIGUEZ, JUAN C.; FARIAS, AGNALDO M.; DE SIQUEIRA, DENISE; DEVLOO, PHILIPPE R. B.. Hierarchical high order finite element spaces in H(div, Omega) x H-1(Omega) fora stabilized mixed formulation of Darcy problem. COMPUTERS & MATHEMATICS WITH APPLICATIONS, v. 80, n. 5, p. 1117-1141, SEP 1 2020. (17/23338-8)

QUINELATO, THIAGO O.; LOULA, ABIMAEL F. D.; CORREA, MAICON R.; ARBOGAST, TODD. Full H(div)-approximation of linear elasticity on quadrilateral meshes based on ABF finite elements. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, v. 347, p. 120-142, APR 15 2019. (17/23338-8)