Optimal Multilevel Methods for H ( grad ) , H ( curl ) , and H ( div ) Systems on Graded and Unstructured Grids

@inproceedings{Xu2009OptimalMM,
  title={Optimal Multilevel Methods for H ( grad ) , H ( curl ) , and H ( div ) Systems on Graded and Unstructured Grids},
  author={Jinchao Xu and Long Chen and Ricardo H. Nochetto},
  year={2009}
}
We give an overview of multilevel methods, such as V-cycle multigrid and BPX preconditioner, for solving various partial differential equations (including H(grad), H(curl) and H(div) systems) on quasi-uniform meshes and extend them to graded meshes and completely unstructured grids. We first discuss the classical multigrid theory on the basis of the method of subspace correction of Xu and a key identity of Xu and Zikatanov. We next extend the classical multilevel methods in H(grad) to graded… CONTINUE READING