Details
| Original language | English |
|---|---|
| Pages (from-to) | 596-615 |
| Number of pages | 20 |
| Journal | Numerical Functional Analysis and Optimization |
| Volume | 31 |
| Issue number | 5 |
| Publication status | Published - May 2010 |
| Externally published | Yes |
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
- Nonoverlapping domain decomposition method (DDM), Quasilinear PDE, Transmission problem
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Computer Science(all)
- Signal Processing
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Control and Optimization
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In: Numerical Functional Analysis and Optimization, Vol. 31, No. 5, 05.2010, p. 596-615.
Research output: Contribution to journal › Article › Research › peer review
}
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 - Nonoverlapping domain decomposition method (DDM)
KW - Quasilinear PDE
KW - Transmission problem
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 - Article
AN - SCOPUS:77954566395
VL - 31
SP - 596
EP - 615
JO - Numerical Functional Analysis and Optimization
JF - Numerical Functional Analysis and Optimization
SN - 0163-0563
IS - 5
ER -