Domain decomposition and partitioning methods for mixed finite element discretizations of the Biot system of poroelasticity

We develop non-overlapping domain decomposition methods for the Biot system of poroelasticity in a mixed form. The solid deformation is modeled with three-field formulation weak stress symmetry. fluid flow Darcy formulation. introduce displacement and pressure Lagrange multipliers on subdomain interfaces to impose weakly continuity normal velocity, respectively. global problem reduced an interface multipliers, which solved by Krylov space iterative method. study both monolithic split methods. In method, coupled displacement-pressure solved, each iteration requiring solution local problems. show that resulting operator positive definite analyze convergence iteration. further drained fixed splittings, case we solve separate problems elasticity solves. stability formulations. Numerical experiments are presented illustrate compare their accuracy efficiency.