Numerical Solution of Coupled Problems in Linear Poroelasticity
Lecturer: Prof. Johannes Kraus
Lecture no.: 327.010
ECTS: 3, hours: 2
Schedule:
Tue, 12.02., 13:45 - 17:00, S2 416-2
Tue, 26.02., 13:45 - 17:00, S2 416-1
Thu, 28.02., 13:45 - 17:00, S2 416-1
Tue, 05.03., 13:45 - 17:00, S2 416-1
Abstract:
In this course, we will present different formulations of Biot’s model. We will address the stability and well-posedness of the continuous
model and derive norm-equivalent preconditioners in the framework of operator preconditioning. The second part of the lecture will be
devoted to strongly mass conservative discretizations based on mixed discontinuous-continuous Galerkin methods. We will prove optimal
error estimates and also derive fully parameter-robust precondtitioners on the discrete level. The third part of the lecture deals with
generalizations of the results covered in the first two parts to multi-permeability poroelasticity problems modeled by the MPET equations.
In the last part of the lecture iterative coupling schemes will be discussed as an alternative for fully implicit methods to solve the quasi-
static Biot- and MPET problems.
Basic knowledge of the finite element method (FEM), in particular, discontinuous Galerkin FEM, is recommended.