Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems

@inproceedings{Wu2006UniformCO,
  title={Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems},
  author={Haijun Wu and Zhiming Chen},
  year={2006}
}
Abstract In this paper we prove the uniform convergence of the standard multigrid V-cycle algorithm with Gauss-Seidel relaxation performed only on new nodes and their “immediate” neighbors for discrete elliptic problems on adaptively refined finite element meshes using the newest vertex bisection algorithm. The proof depends on sharp estimates on the relationship of local mesh sizes and a new stability estimate for the space decomposition based on Scott-Zhang interpolation operator. Extensive… CONTINUE READING

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