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Multigrid techniques for finite elements on locally refined meshes. (English) Zbl 1051.65117
Summary: We investigate multigrid algorithms on locally refined quadrilateral meshes. In contrast to a standard multigrid algorithm, where the hierarchy of meshes is generated by global refinement, we suppose that the finest mesh results from an adaptive refinement algorithm using bisection and ‘hanging nodes’. We discuss the additional difficulties introduced by these meshes and investigate two different algorithms. The first algorithm uses merely the local refinement regions per level, leading to optimal solver complexity even on strongly locally refined meshes, whereas the second one constructs the lower level meshes by agglomeration of cells. In this note, we are mainly interested in implementation details and practical performance of the two multigrid schemes.

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
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65Y20 Complexity and performance of numerical algorithms
Software:
PLTMG
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