An auxiliary space multigrid preconditioner for the weak Galerkin method

In this paper, the authors constructed an auxiliary space multigrid preconditioner for the weak Galerkin finite element method for second-order diffusion equations, discretized on simplicial 2D or 3D meshes. The idea of the auxiliary space multigrid preconditioner is to use an auxiliary space as a "coarse" space in the multigrid algorithm, where the discrete problem in the auxiliary space can be easily solved by an existing solver. In this construction, the authors conveniently use the $H^1$ conforming piecewise linear finite element space as an auxiliary space. The main technical difficulty is to build the connection between the weak Galerkin discrete space and the $H^1$ conforming piecewise linear finite element space. The authors successfully constructed such an auxiliary space multigrid preconditioner for the weak Galerkin method, as well as a reduced system of the weak Galerkin method involving only the degrees of freedom on edges/faces. The preconditioned systems are proved to have condition numbers independent of the mesh size. Numerical experiments are conducted to support the theoretical results.

• Publication year

  2014

• Venue

  Computers and Mathematics with Applications

• Publication date

  2014-10-04

• Fields of study

  Mathematics, Computer Science, Engineering

• Identifiers
  DOI 10.1016/j.camwa.2015.04.016arXiv 1410.1012
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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