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Volume 20, Issue 5
Rate of Convergence of Schwarz Alternating Method for Time-Dependent Convection-Diffusion Problem

Jian-Wei Hu & Cai-Hua Wang

J. Comp. Math., 20 (2002), pp. 479-490.

Published online: 2002-10

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  • Abstract

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.

  • Keywords

Rate of convergence, Schwarz alternating method, Convection-diffusion problem.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-20-479, author = {Hu , Jian-Wei and Wang , Cai-Hua}, title = {Rate of Convergence of Schwarz Alternating Method for Time-Dependent Convection-Diffusion Problem}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {5}, pages = {479--490}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8933.html} }
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 -

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.

Hu , Jian-Wei and Wang , Cai-Hua. (2002). Rate of Convergence of Schwarz Alternating Method for Time-Dependent Convection-Diffusion Problem. Journal of Computational Mathematics. 20 (5). 479-490. doi:
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