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Advanced Numerical Methods in the Mathematical Sciences

Carmen Rodrigo, University of Zaragoza (Spain)
Stable Discretizations and Multigrid Solution of Biot's Consolidation Problem


This work deals with the numerical solution of the Biot's consolidation problem. The emphasis here is on the stable discretization and the highly efficient solution of the resulting algebraic system of equations, which is of saddle point type. On the one hand, stabilized linear finite element schemes providing oscillation-free solutions for this model are proposed and theoretically analyzed. On the other hand, a monolithic multigrid method is considered for the solution of the resulting system of equations after discretization by using the stabilized scheme. Since this system is of saddle point type, special smoothers of "Vanka"-type have to be considered. This multigrid method is designed with the help of a special local Fourier analysis that takes into account the specific characteristics of the considered block-relaxations. Results from this analysis are presented and compared with those experimentally computed.