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A multilevel preconditioner for the mortar method for nonconforming \(P_{1}\) finite element. (English) Zbl 1203.65259

The paper is concerned with the mortar method for nonconforming \(P_1\) elements or Crouzeix-Raviart elements, illustrated for the Poisson equation on the unit square. A multilevel preconditioner is proposed which is such that the condition number of the preconditioned system is independent of the mesh size. Some numerical tests illustrate and support the results.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
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