On the Equivalence of Transmission Problems in Nonoverlapping Domain Decomposition Methods for Quasilinear PDEs
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Authors
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 language | English |
|---|---|
| Journal | Numerical Functional Analysis and Optimization |
| Volume | 31 |
| Issue number | 5 |
| Pages (from-to) | 596-615 |
| Number of pages | 20 |
| DOIs | |
| Publication status | Published - 05.2010 |
| Externally published | Yes |
- Mathematics - Nonoverlaping domain decomposition method (DDM), Quasilinear PDE, Transmission problem, AMS Subject Classification