Large-Scale Scientific Computing

The paper concerns porous media flow in rigid or deformable matrix. It starts with stationary Darcy flow, but the main interest is in extending Darcy problem to involve time dependent behaviour and deformation of the matrix. The considered problems are discretized by mixed FEM in space and stable time discretization methods as backward Euler and second order Radau methods. The discretization leads to time stepping methods which involve solution of a linear system within each time step. The main focus of the paper is then devoted to the construction of suitable preconditioners for these Euler and Radau systems. The paper presents also numerical experiments for illustration of efficiency of the suggested numerical algorithms.

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