Preconditioning discretizations of systems of partial differential equations. (Q2889367)
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scientific article; zbMATH DE number 6043421
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Preconditioning discretizations of systems of partial differential equations. |
scientific article; zbMATH DE number 6043421 |
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7 June 2012
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preconditionning
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finite element method
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discrete system
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Krylov space methods
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saddle point problems
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(singularly perturbed) problems
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Laplace operator
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Maxwell problem
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Stokes problem
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reaction-diffusion problem
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Reissner-Mindlin plate model
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optimal control problem
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Preconditioning discretizations of systems of partial differential equations. (English)
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This review paper surveys an abstract approach for construction of preconditioners for differential operators in the setting of Hilbert spaces. First, the idea is presented in the context of Krylov space methods. Then, the authors concentrate on abstract saddle point problems, parameter-dependent (singularly perturbed) problems, and on a general approach for preconditioning finite element systems. The paper contains a number of examples including the Laplace operator, a Maxwell problem, Stokes problem, reaction-diffusion problem, Reissner-Mindlin plate model and optimal control problem.
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