Continuous preconditioners for the mixed Poisson problem

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Continuous preconditioners for the mixed Poisson problem. / Hannukainen, Antti.

In: BIT Numerical Mathematics, Vol. 52, No. 1, 03.2012, p. 65-83.

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@article{3a776cf161f94d7d824c342adb4360ea,
title = "Continuous preconditioners for the mixed Poisson problem",
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.",
keywords = "Finite element method, Mixed Poisson problem, Preconditioning",
author = "Antti Hannukainen",
year = "2012",
month = "3",
doi = "10.1007/s10543-011-0346-0",
language = "English",
volume = "52",
pages = "65--83",
journal = "BIT - Numerical Mathematics",
issn = "0006-3835",
publisher = "Springer Netherlands",
number = "1",

}

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TY - JOUR

T1 - Continuous preconditioners for the mixed Poisson problem

AU - Hannukainen, Antti

PY - 2012/3

Y1 - 2012/3

N2 - 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.

AB - 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.

KW - Finite element method

KW - Mixed Poisson problem

KW - Preconditioning

UR - http://www.scopus.com/inward/record.url?scp=84857684691&partnerID=8YFLogxK

U2 - 10.1007/s10543-011-0346-0

DO - 10.1007/s10543-011-0346-0

M3 - Article

VL - 52

SP - 65

EP - 83

JO - BIT - Numerical Mathematics

JF - BIT - Numerical Mathematics

SN - 0006-3835

IS - 1

ER -

ID: 12920778