TY - JOUR
T1 - Rate of Convergence of Schwarz Alternating Method for Time-Dependent Convection-Diffusion Problem
AU - Hu , Jian-Wei
AU - Wang , Cai-Hua
JO - Journal of Computational Mathematics
VL - 5
SP - 479
EP - 490
PY - 2002
DA - 2002/10
SN - 20
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8933.html
KW - Rate of convergence, Schwarz alternating method, Convection-diffusion problem.
AB - <p style="text-align: justify;">This paper provides a theoretical justification to a overlapping domain decomposition method applied to the solution of time-dependent convection-diffusion problems. The method is based on the partial upwind finite element scheme and the discrete strong maximum principle for steady problem. An error estimate in $L^\infty(0,T;L^\infty(\Omega))$ is obtained and the fact that convergence factor $\rho(\tau,h)\rightarrow 0$ exponentially as $\tau,h\rightarrow 0$ is also proved under some usual conditions.</p>