TY - JOUR
T1 - Partition Property of Domain Decomposition Without Ellipticity
AU - Mu , Mo
AU - Huang , Yun-Qing
JO - Journal of Computational Mathematics
VL - 4
SP - 423
EP - 432
PY - 2001
DA - 2001/08
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8994.html
KW - Partition property, Domain decomposition, Non-ellipticity, Degenerate parabolic problems, Time-dependent Ginzburg-Landau model, Superconductivity, Preconditioning, Schwarz algorithms.
AB - <p style="text-align: justify;">Partition property plays a central role in domain decomposition methods. Existing theory essentially assumes certain ellipticity. We prove the partition property for problems without ellipticity which are of practical importance. Example applications include implicit schemes applied to degenerate parabolic partial differential equations arising from superconductors, superfluids and liquid crystals. With this partition property, Schwarz algorithms can be applied to general non-elliptic problems with an $h$-independent optimal convergence rate. Application to the time-dependent Ginzburg-Landau model of superconductivity is illustrated and numerical results are presented. &nbsp;</p>