On the Equivalence of Transmission Problems in Nonoverlapping Domain Decomposition Methods for Quasilinear PDEs
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In: Numerical Functional Analysis and Optimization, Vol. 31, No. 5, 05.2010, p. 596-615.
Research output: Journal contributions › Journal articles › Research › peer-review
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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 -