The analysis of intergrid transfer operators and multigrid methods for nonconforming finite elements.

*(English)*Zbl 0890.65126The purpose of this paper is to analyze intergrid transfer operators and their iterates for some nonconforming finite elements used for discretizations of second- and fourth-order elliptic problems and to discuss convergence of two classes of multigrid methods using these elements. The first class is the usual one, which uses discrete equations on all levels which are defined by the same discretization.

The second class of multigrid methods was recently introduced by the author [On the convergence of Galerkin-multigrid methods for nonconforming finite elements, Technical Report # 96-02, Southern Methodist University, Texas (1996)] and is based on the Galerkin approach. Convergence results for partial differential problems with less than full elliptic regularity and without any elliptic regularity are considered.

The second class of multigrid methods was recently introduced by the author [On the convergence of Galerkin-multigrid methods for nonconforming finite elements, Technical Report # 96-02, Southern Methodist University, Texas (1996)] and is based on the Galerkin approach. Convergence results for partial differential problems with less than full elliptic regularity and without any elliptic regularity are considered.

Reviewer: P.ChocholatĂ˝ (Bratislava)

##### MSC:

65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |

35J25 | Boundary value problems for second-order elliptic equations |

35J40 | Boundary value problems for higher-order elliptic equations |