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We consider L-scheme and Newton based solvers for Biot model under small orlarge deformation. The mechanical deformation follows the Saint Venant-Kirchoffconstitutive law. Further, the fluid compressibility is assumed to benonlinear. A Lagrangian frame of reference is used to keep track of thedeformation. We perform an implicit discretization in time (backward Euler) andpropose two linearization schemes for solving the nonlinear problems appearingwithin each time step: Newton's method and L-scheme. The linearizations areused monolithically or in combination with a splitting algorithm. The resultingschemes can be applied for any spatial discretization. The convergences of allschemes are shown analytically for cases under small deformation. Illustrativenumerical examples are presented to confirm the applicability of the schemes,in particular, for large deformation.

Iterative solvers for Biot model under small and large deformation