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

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