Multigrid methods for the parameter dependent problems


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  • Speaker(s)Hui Zheng (Peking University)
  • DateFrom 2014-06-26 To 2014-06-26
  • VenueRoom 77201 at #78 courtyard, Beijing International Center for Mathematical Research

Speaker: Hui Zheng (Peking University)

Time: Thu, 06/26/2014 - 14:45

Place: Room 77201 at #78 courtyard, Beijing International Center for Mathematical Research

Abstract: We investigate multigrid methods for the parameter dependent problems. We construct and analyze multigrid methods from the viewpoint of space decomposition and subspace correction. For parallel subspace correction methods, we develop a framework for the nearly singular problems and use this framework to analyze actual problems.

For the elliptic problems with jumps in coefficients, we construct a modified multigrid method. For both successive subspace correction methods and parallel subspace correction methods, we prove the uniform convergence of our modified multigrid method. For the planar nearly incompressible elasticity problem with the Scott-Vogelius finite element discretization, we prove the uniform convergence of the conjugate gradient method with the BPX-type preconditioner.

We also study the multigrid methods on adaptive refined finite element meshes. We introduce a new local projection and prove the uniform convergence of the multilevel algorithm which performs relaxation on new nodes and their immediate neighbors. By this techniques, we can study the parameter dependent problems on the adaptive meshes.


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