On the Equivalence of Transmission Problems in Nonoverlapping Domain Decomposition Methods for Quasilinear PDEs

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On the Equivalence of Transmission Problems in Nonoverlapping Domain Decomposition Methods for Quasilinear PDEs. / Schreiber, Stephan; Hochmuth, Reinhard.
in: Numerical Functional Analysis and Optimization, Jahrgang 31, Nr. 5, 05.2010, S. 596-615.

Publikation: Beiträge in ZeitschriftenZeitschriftenaufsätzeForschungbegutachtet

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@article{a3d26a45345947ea9023f0da9c95690e,
title = "On the Equivalence of Transmission Problems in Nonoverlapping Domain Decomposition Methods for Quasilinear PDEs",
abstract = "We consider a general quasilinear model problem of second order in divergence form on a Lipschitz domain, where the latter is divided arbitrarily in finitely many Lipschitz subdomains. Regarding this decomposition, several transmission problems, being equivalent to the model problem in a weak sense, are constructed. Thereby, no regularity assumption on the solution beyond H 1 is necessary. Furthermore, we do not need additional smoothness conditions on the boundaries of the subdomains and decompositions with crosspoints are admissible.",
keywords = "Mathematics, Nonoverlaping domain decomposition method (DDM), Quasilinear PDE, Transmission problem, AMS Subject Classification",
author = "Stephan Schreiber and Reinhard Hochmuth",
year = "2010",
month = may,
doi = "10.1080/01630563.2010.490625",
language = "English",
volume = "31",
pages = "596--615",
journal = "Numerical Functional Analysis and Optimization",
issn = "1532-2467",
publisher = "Taylor & Francis",
number = "5",

}

RIS

TY - JOUR

T1 - On the Equivalence of Transmission Problems in Nonoverlapping Domain Decomposition Methods for Quasilinear PDEs

AU - Schreiber, Stephan

AU - Hochmuth, Reinhard

PY - 2010/5

Y1 - 2010/5

N2 - We consider a general quasilinear model problem of second order in divergence form on a Lipschitz domain, where the latter is divided arbitrarily in finitely many Lipschitz subdomains. Regarding this decomposition, several transmission problems, being equivalent to the model problem in a weak sense, are constructed. Thereby, no regularity assumption on the solution beyond H 1 is necessary. Furthermore, we do not need additional smoothness conditions on the boundaries of the subdomains and decompositions with crosspoints are admissible.

AB - We consider a general quasilinear model problem of second order in divergence form on a Lipschitz domain, where the latter is divided arbitrarily in finitely many Lipschitz subdomains. Regarding this decomposition, several transmission problems, being equivalent to the model problem in a weak sense, are constructed. Thereby, no regularity assumption on the solution beyond H 1 is necessary. Furthermore, we do not need additional smoothness conditions on the boundaries of the subdomains and decompositions with crosspoints are admissible.

KW - Mathematics

KW - Nonoverlaping domain decomposition method (DDM)

KW - Quasilinear PDE

KW - Transmission problem

KW - AMS Subject Classification

UR - http://www.scopus.com/inward/record.url?scp=77954566395&partnerID=8YFLogxK

U2 - 10.1080/01630563.2010.490625

DO - 10.1080/01630563.2010.490625

M3 - Journal articles

VL - 31

SP - 596

EP - 615

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

SN - 1532-2467

IS - 5

ER -

DOI