3 papers
math.NA2026
A family of mixed-mixed strongly conservative finite element methods for Biot's model of consolidation
Qingguo Hong, Johannes Kraus, Maria Lymbery
We consider a four-field formulation of Biot's quasi-static model of consolidation with the (effective) elastic stress, the solid displacement, the fluid flux and the fluid pressur…
math.NA2025
Fitted norm preconditioners for the Hodge Laplacian in mixed form
Wietse M. Boon, Johannes Kraus, Tomáš Luber +1
We use the practical framework for abstract perturbed saddle point problems recently introduced by Hong et al. to analyze the mixed formulation of the Hodge Laplace problem. We com…
math.NA2025
Time-continuous strongly conservative space-time finite element methods for the dynamic Biot model
Johannes Kraus, Maria Lymbery, Kevin Osthues
We consider the dynamic Biot model (see [Biot, M. A. J. Appl. Phys. 33, 1482--1498 (1962)]) describing the interaction between fluid flow and solid deformation including wave propa…