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Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 491-505.
Published online: 2018-11
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An effective method is proposed for interface problems by combining the domain decomposition method and the collocation method. The main idea is to split the whole domain into two non-overlapped sub-domains and enforce the interface conditions to obtain two sub-problems. Each sub-problem is solved by the collocation method. And a simple iterative algorithm is presented to achieve the jump conditions at the interface. The method provided can be used to solve interface problems with both linear and a special type of non-linear jump conditions. Numerical experiments reveal that our method is fourth-order accurate for interface problems.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2018.m1667}, url = {http://global-sci.org/intro/article_detail/nmtma/12441.html} }An effective method is proposed for interface problems by combining the domain decomposition method and the collocation method. The main idea is to split the whole domain into two non-overlapped sub-domains and enforce the interface conditions to obtain two sub-problems. Each sub-problem is solved by the collocation method. And a simple iterative algorithm is presented to achieve the jump conditions at the interface. The method provided can be used to solve interface problems with both linear and a special type of non-linear jump conditions. Numerical experiments reveal that our method is fourth-order accurate for interface problems.