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

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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.
Original languageEnglish
JournalNumerical Functional Analysis and Optimization
Volume31
Issue number5
Pages (from-to)596-615
Number of pages20
DOIs
Publication statusPublished - 05.2010
Externally publishedYes

    Research areas

  • Mathematics - Nonoverlaping domain decomposition method (DDM), Quasilinear PDE, Transmission problem, AMS Subject Classification

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