PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Fei Wang, Toan Nguyen, Stephanie Zerby, Mark Levi, Victor Nistor, Jinchao Xu, Ludmil Zikatanov, Chun Liu.

Title:Numerical solution of a poroelasticity problem by stabilized finite element method and multigrid
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Carmen Rodrigo, Universidad de Zaragoza
Abstract:
The classical quasi-static Biot model for soil consolidation, describes the time dependent interaction between the deformation of an elastic porous material and the fluid flow inside of it. This model can be formulated as a system of partial differential equations for the displacement of the solid and the pressure of the fluid. Due to a lack of compatibility between the boundary and initial conditions, a transient boundary layer appears in the pressure field. In such case standard (non stabilized) approximation schemes produce non-physical oscillations in the numerical solution. Different stabilization strategies have been proposed to overcome this. We consider a stabilized linear finite element scheme for the poroelasticity model, based on the perturbation of the flow equation. Such scheme uses low order (piece-wise linear) finite element spaces for both displacements and pressure. The stabilization term results in numerical solution without spurious oscillations, independently of the discretization parameters. The resulting linear algebraic system is of saddle point type and we address its efficient solution by a geometric multigrid method. We also present local Fourier analysis of the components of the multigrid algorithm on simplicial (triangular) grids.

Room Reservation Information

Room Number:MB106
Date:03 / 17 / 2014
Time:02:30pm - 03:30pm