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A multigrid method for a parameter dependent problem in solid mechanics. (English) Zbl 0665.65077
In the finite element calculations of problems in solid mechanics the method of selected reduced integration (SRI) is frequently used to eliminate locking phenomena. Often SRI is equivalent to the application of a mixed method. When multigrid methods are applied the formulation as a mixed method is by far superior. This is shown by an analysis of the Timoshenko beam. It is proved that the convergence rate of the multigrid method for the mixed model is independent of the penalty parameter as the latter tends to zero. To this end a general theory for mixed methods with penalty terms is presented. The theoretical results are verified by numerical results for the mixed method and for the displacement model with SRI.
Reviewer: D.Braess

MSC:
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74S05 Finite element methods applied to problems in solid mechanics
65F10 Iterative numerical methods for linear systems
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