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

Research output: Journal contributions › Journal articles › Research › peer-review

Standard

On the Equivalence of Transmission Problems in Nonoverlapping Domain Decomposition Methods for Quasilinear PDEs. / Schreiber, Stephan; Hochmuth, Reinhard.
In: Numerical Functional Analysis and Optimization, Vol. 31, No. 5, 05.2010, p. 596-615.

Research output: Journal contributions › Journal articles › Research › peer-review

Harvard

Schreiber, S & Hochmuth, R 2010, 'On the Equivalence of Transmission Problems in Nonoverlapping Domain Decomposition Methods for Quasilinear PDEs', Numerical Functional Analysis and Optimization, vol. 31, no. 5, pp. 596-615. https://doi.org/10.1080/01630563.2010.490625

APA

Schreiber, S., & Hochmuth, R. (2010). On the Equivalence of Transmission Problems in Nonoverlapping Domain Decomposition Methods for Quasilinear PDEs. Numerical Functional Analysis and Optimization, 31(5), 596-615. https://doi.org/10.1080/01630563.2010.490625

Vancouver

Schreiber S, Hochmuth R. On the Equivalence of Transmission Problems in Nonoverlapping Domain Decomposition Methods for Quasilinear PDEs. Numerical Functional Analysis and Optimization. 2010 May;31(5):596-615. doi: 10.1080/01630563.2010.490625

Bibtex

@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 and Francis Ltd.",
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 -

Other publications by the same author(s)

Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings

Göller, R. (Editor), Biehler, R., Hochmuth, R. K. & Rück, H.-G., 2017, Kassel: Kompetenzentrum Hochschuldidaktik Mathematik - Universität Kassel. 509 p. (khdm-Report; vol. 2017, no. 05)

Research output: Books and anthologies › Conference proceedings › Research

Mathematik im Ingenieurwissenschaftsstudium – Ansätze zu einer fachbezogenen Kompetenzmodellierung

Hochmuth, R. K. & Schreiber, S., 2014, TeachING-LearnING.EU Tagungsband: movING Forward; Engineering Education from vision to mission. Tekkaya, A. E., Jeschke, S. & Petermann, M. (eds.). Technische Universität Dortmund, p. 68-76 9 p.

Research output: Contributions to collected editions/works › Article in conference proceedings › Research › peer-review

Mit Werkzeugen Mathematik und Stochastik lernen

Wassong, T., Frischemeier, D., Fischer, P. R., Hochmuth, R. & Bender, P., 2014, Wiesbaden: Springer Spektrum. 497 p.

Research output: Books and anthologies › Book

Vorstellung eines Fragebogens zur Erfassung von Lernstrategien in mathematikhaltigen Studiengängen.

Liebendörfer, M., Hochmuth, R. K., Schreiber, S., Göller, R., Kolter, J., Biehler, R., Kortemeyer, J. & Ostsieker, L., 2014, Beiträge zum Mathematikunterricht 2014: Beiträge zur 48. Jahrestagung der Gesellschaft für Didaktik der Mathematik vom 10. bis 14. März 2014 in Koblenz. Roth, J. & Ames, J. (eds.). WTM - Verlag für wissenschaftliche Texte und Medien, Vol. 2. p. 739-742 4 p.

Research output: Contributions to collected editions/works › Article in conference proceedings › Research

Blended-Learning Brückenkurs Mathematik für Wirtschaftswissenschaftler.

Goguadze, G. & Hochmuth, R., 25.11.2013, Mathematik im Übergang Schule / Hochschule und im ersten Studienjahr: Extended Abstracts zur 2. khdm-Arbeitstagung. Hoppenbrock, A., Schreiber, S., Göller, R., Biehler, R., Büchler, B., Hochmuth, R. & Rück, H.-G. (eds.). Universitätsbibliothek Kassel, Vol. khdm-Report 13-01. p. 63-64 2 p. (KHDM-Report; vol. 13, no. 01).

Research output: Contributions to collected editions/works › Other › Research

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