Exame de Qualificação: High order space-time discretizations for biot’s consolidation problem

Aluno: Ismael de Souza Ledoino

Orientadores:
Abimael Fernando Dourado Loula - Laboratório Nacional de Computação Científica - LNCC

Banca Examinadora:
João Nisan Correia Guerreiro - Laboratório Nacional de Computação Científica - LNCC (presidente)
Alexandre Loureiro Madureira - Laboratório Nacional de Computação Científica - LNCC
Eduardo Gomes Dutra do Carmo - Universidade Federal do Rio de Janeiro - UFRJ
Maicon Ribeiro Correa - UNICAMP

Suplentes:
Sandra Mara Cardoso Malta - Laboratório Nacional de Computação Científica - LNCC

Resumo:WE PROPOSE A NEW MIXED HYBRID DISCONTINUOUS GALERKIN METHOD FOR BIOT'S CONSOLIDATION PROBLEM.
THE METHOD IS ARBITRARILY HIGH ORDER IN SPACE AND TIME, AND THE NEW TIME DISCRETIZATION SCHEME IS APPLICABLE TO
ANY OTHER TIME-DEPENDENT PROBLEM. THE DISCRETIZATION IN SPACE CONSISTS OF A MIXED PROBLEM IN THREE MAIN
UNKNOWNS: DISPLACEMENT, PORE PRESSURE AND HYDROSTATIC PRESSURE, BEING THE LATTER INTRODUCED MAINLY FOR THE
PURPOSE OF GENERATING A LOCKING-FREE METHOD. THE HYBRIDIZATION IS MADE THROUGH THE INSERTION OF CONTINUOUS
OR DISCONTINUOUS LAGRANGE MULTIPLIERS IDENTIFIED WITH THE TRACE OF THE DISPLACEMENT AND PORE PRESSURE FIELDS
AT THE SKELETON OF THE MESH (WHICH CAN BE CURVED). OUR ANALYSIS IN SPACE HANDLES REDUCED ORDER DISCONTINUOUS
LAGRANGE MULTIPLIERS, WHICH ARE POSSIBLE WITH AN USE OF PROJECTION OPERATORS. FOR THE DISCRETIZATION IN TIME,
WE GENERALIZE THE SECOND ORDER CONVERGENT CRANK-NICOLSON SCHEME TO THE ARBITRARY ORDER CONVERGENT MSTS
SCHEME, WHICH IS AN IMPLICIT MULTI-STEP TWO-STAGE METHOD THAT IS ALSO UNCONDITIONALLY STABLE. THE NUMERICAL
ANALYSIS OF THE SCHEME IS IN PROGRESS, BUT WE PRESENT PARTIAL RESULTS. NUMERICAL EXPERIMENTS ARE PERFORMED TO
SHOW THE OPTIMAL CONVERGENCE RATES IN SPACE AND TIME, THE LOCKING-FREE PROPERTY OF THE SPACE DISCRETIZATION
AND THE UNCONDITIONAL STABILITY OF THE TIME DISCRETIZATION.

Para assistir acesse: https://us02web.zoom.us/j/86495264297?pwd=VnhYeDYzQlRqbGNSR25tc0J2N2Z5Zz09