EVENTO
High Order Space and Time Discretizations to Biots Consolidation Problem
Tipo de evento: Defesa de Tese de Doutorado
We propose a high order space and time discretization to Biots consolidation problem, composed of a mixedhybrid discontinuous Galerkin (HDG) method in space and a modified Runge-Kutta (MRK) method in time.The HDG method is a mixed problem in three main unknowns: displacement, pore pressure and hydrostaticpressure, being the latter introduced mainly for the purpose of generating a locking-free method. Thehybridization is made through the insertion of continuous (EDG) or discontinuous (HDG) Lagrange multipliersidentified with the trace of the displacement and pore pressure fields at the skeleton of the mesh. Ouranalysis in space handles reduced order discontinuous Lagrange multipliers, which are possible with an use ofprojection operators. For the discretization in time, we generalize the second order convergent Crank-Nicolson scheme to an arbitrary high order convergent Runge-Kutta scheme, known as Gauss-Legendrecollocation method (GLC). The way we derive the GLC method suggests a more efficient way ofimplementing it for PDEs, and the conversion formula is applicable to many other RK methods, includingsome explicit ones. The numerical analysis of the semi-discrete problem is devised, and numerical estimatesare also obtained for the fully discrete problem in which implicit Euler and Crank-Nicolson schemes are used.Numerical experiments are performed to show the optimal convergence rates in space and time, thelocking-free property of the space discretization and the unconditional stability of the time discretization.Para acessar:Link: https://us02web.zoom.us/webinar/register/WN_bwBctRD8RR6ffAEQ4AdmeQ
Data Início: 19/08/2022 Hora: 14:00 Data Fim: 19/08/2022 Hora: 17:00
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Webinar
Aluno: Ismael de Souza Ledoino - Laboratório Nacional de Computação Científica - LNCC
Orientador: Abimael Fernando Dourado Loula - Laboratório Nacional de Computação Científica - LNCC
Participante Banca Examinadora: Cristiane Oliveira de Faria - Universidade do Estado do Rio de Janeiro - UERJ Eduardo Gomes Dutra do Carmo - Universidade Federal do Rio de Janeiro - UFRJ Maicon Ribeiro Correa - Universidade Estadual de Campinas - UNICAMP Sandra Mara Cardoso Malta - Laboratório Nacional de Computação Científica - LNCC
Suplente Banca Examinadora: Alexandre Loureiro Madureira - Laboratório Nacional de Computação Científica - LNCC Rodrigo Weber dos Santos - Universidade Federal de Juiz de Fora - UFJF
