Continuous preconditioners for the mixed Poisson problem

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Abstract

In this note, we show how to apply preconditioners designed for piecewise linear finite element discretizations of the Poisson problem as preconditioners for the mixed problem. Our preconditioner can be applied both to the original and to the reduced Schur complement problem. Combined with a suitable iterative method, the number of iterations required to solve the preconditioned system will have the same dependency on the mesh size as for the preconditioner applied to the Poisson problem. The presented theory is demonstrated by numerical examples.

Details

Original languageEnglish
Pages (from-to)65-83
Number of pages19
JournalBIT Numerical Mathematics
Volume52
Issue number1
Publication statusPublished - Mar 2012
MoE publication typeA1 Journal article-refereed

    Research areas

  • Finite element method, Mixed Poisson problem, Preconditioning

ID: 12920778