• Corpus ID: 18722277

1 Preconditioning in H ( div ) and Applications

@inproceedings{Arnold20011PI,
  title={1 Preconditioning in H ( div ) and Applications},
  author={Douglas N. Arnold and Richard S. Falk and Ragnar Winther},
  year={2001}
}
Summarizing the work of [AFW97], we show how to construct preconditioners using domain decomposition and multigrid techniques for the system of linear algebraic equations which arises from the finite element discretization of boundary value problems associated to the differential operator I − grad div. These preconditioners are shown to be spectrally equivalent to the inverse of the operator and thus may be used to precondition iterative methods so that any given error reduction may be achieved… 

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SHOWING 1-5 OF 5 REFERENCES
PRECONDITIONING IN H (div) AND APPLICATIONS
TLDR
These preconditioners are shown to be spectrally equivalent to the inverse of the operator and may be used to preconditions iterative methods so that any given error reduction may be achieved in a finite number of iterations, with the number independent of the mesh discretization.
Iterative Methods by Space Decomposition and Subspace Correction
TLDR
A unified theory for a diverse group of iterative algorithms, such as Jacobi and Gauss–Seidel iterations, diagonal preconditioning, domain decomposition methods, multigrid methods,Multilevel nodal basis preconditionsers and hierarchical basis methods, is presented by using the notions of space decomposition and subspace correction.
First-order system least squares for second-order partial differential equations: part I
TLDR
The least-squares approach developed here applies directly to convection--diffusion--reaction equations in a unified way and also admits a fast multigrid solver, historically a missing ingredient in least-Squares methodology.
Least-squares mixed finite elements for second-order elliptic problems
A theoretical analysis of a least-squares mixed finite element method for second-order elliptic problems in two- and three-dimensional domains is presented. It is proved that the method is not subj...
DD9 Proceedings Editor Petter Bjørstad
  • DD9 Proceedings Editor Petter Bjørstad
  • 1996