Abstract
This paper deals with the 2D system of incompressible poroelasticity equations in which an artificial stabilization term has been added to the discretization on collocated grids. Two issues are discussed: It is proved and shown that the additional term indeed brings stability and does not spoil the second order accurate convergence. Secondly, various smoothers are examined in order to find an optimal multigrid method for the discrete system of equations. Numerical experiments confirm the stability and the second order accuracy, as well as fast multigrid convergence for a realistic poroelasticity experiment.
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