Conservative stable discretizations and parameter-robust preconditioners for three-field formulation of Biot’s consolidation model

Priv.-Doz. Dr. Johannes Kraus

March 6, 2018, 3:30 p.m. S2 416-1

Poroelastic models describe the mechanical deformation and the fluid flow in porous media. They have a wide range of applications
in medicine, biophysics and geosciences. In this talk we analyze the stability of a classical three-field formulation of Biot’s consolidation model
where the unknown variables are the displacements, the fluid flux (Darcy velocity), and the pore pressure.
The key to establish the parameter-robust inf-sup stability of the continuous problem is the choice of proper parameter-dependent norms.
This allows for the construction of uniform block diagonal preconditioners in the framework of operator preconditioning. Stable discretizations
that meet the required conditions for exact (pointwise) conservation of mass are discussed and corresponding optimal error estimates proved.
This is joint work with Qingguo Hong from Penn State University, USA.