Volume 32, Issue 4
On the Optimal Convergence Rate of a Robin-Robin Domain Decomposition Method

J. Comp. Math., 32 (2014), pp. 456-475.

Published online: 2014-08

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• Abstract

In this work, we solve a long-standing open problem: Is it true that the convergence rate of the Lions' Robin-Robin nonoverlapping domain decomposition (DD) method can be constant, independent of the mesh size $h?$ We closed this old problem with a positive answer. Our theory is also verified by numerical tests.

• Keywords

Finite element, Robin-Robin domain decomposition, Convergence rate.

65N30, 65M60.

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@Article{JCM-32-456, author = {}, title = {On the Optimal Convergence Rate of a Robin-Robin Domain Decomposition Method}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {4}, pages = {456--475}, abstract = {

In this work, we solve a long-standing open problem: Is it true that the convergence rate of the Lions' Robin-Robin nonoverlapping domain decomposition (DD) method can be constant, independent of the mesh size $h?$ We closed this old problem with a positive answer. Our theory is also verified by numerical tests.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1403-m4391}, url = {http://global-sci.org/intro/article_detail/jcm/9897.html} }
TY - JOUR T1 - On the Optimal Convergence Rate of a Robin-Robin Domain Decomposition Method JO - Journal of Computational Mathematics VL - 4 SP - 456 EP - 475 PY - 2014 DA - 2014/08 SN - 32 DO - http://doi.org/10.4208/jcm.1403-m4391 UR - https://global-sci.org/intro/article_detail/jcm/9897.html KW - Finite element, Robin-Robin domain decomposition, Convergence rate. AB -

In this work, we solve a long-standing open problem: Is it true that the convergence rate of the Lions' Robin-Robin nonoverlapping domain decomposition (DD) method can be constant, independent of the mesh size $h?$ We closed this old problem with a positive answer. Our theory is also verified by numerical tests.

Wenbin Chen, Xuejun Xu & Shangyou Zhang. (1970). On the Optimal Convergence Rate of a Robin-Robin Domain Decomposition Method. Journal of Computational Mathematics. 32 (4). 456-475. doi:10.4208/jcm.1403-m4391
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