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 -