Volume 8, Issue 3
Local Multilevel Method on Adaptively Refined Meshes for Elliptic Problems with Smooth Complex Coefficients

Shishun Li, Xinping Shao & Zhiyong Si

Numer. Math. Theor. Meth. Appl., 8 (2015), pp. 336-355.

Published online: 2015-08

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  • Abstract

In this paper, a local multilevel algorithm is investigated for solving linear systems arising from adaptive finite element approximations of second order elliptic problems with smooth complex coefficients. It is shown that the abstract theory for local multilevel algorithm can also be applied to elliptic problems whose dominant coefficient is complex valued. Assuming that the coarsest mesh size is sufficiently small, we prove that this algorithm with Gauss-Seidel smoother is convergent and optimal on the adaptively refined meshes generated by the newest vertex bisection algorithm. Numerical experiments are reported to confirm the theoretical analysis.

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@Article{NMTMA-8-336, author = {}, title = {Local Multilevel Method on Adaptively Refined Meshes for Elliptic Problems with Smooth Complex Coefficients}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2015}, volume = {8}, number = {3}, pages = {336--355}, abstract = {

In this paper, a local multilevel algorithm is investigated for solving linear systems arising from adaptive finite element approximations of second order elliptic problems with smooth complex coefficients. It is shown that the abstract theory for local multilevel algorithm can also be applied to elliptic problems whose dominant coefficient is complex valued. Assuming that the coarsest mesh size is sufficiently small, we prove that this algorithm with Gauss-Seidel smoother is convergent and optimal on the adaptively refined meshes generated by the newest vertex bisection algorithm. Numerical experiments are reported to confirm the theoretical analysis.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.m1323}, url = {http://global-sci.org/intro/article_detail/nmtma/12413.html} }
TY - JOUR T1 - Local Multilevel Method on Adaptively Refined Meshes for Elliptic Problems with Smooth Complex Coefficients JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 336 EP - 355 PY - 2015 DA - 2015/08 SN - 8 DO - http://doi.org/10.4208/nmtma.2015.m1323 UR - https://global-sci.org/intro/article_detail/nmtma/12413.html KW - AB -

In this paper, a local multilevel algorithm is investigated for solving linear systems arising from adaptive finite element approximations of second order elliptic problems with smooth complex coefficients. It is shown that the abstract theory for local multilevel algorithm can also be applied to elliptic problems whose dominant coefficient is complex valued. Assuming that the coarsest mesh size is sufficiently small, we prove that this algorithm with Gauss-Seidel smoother is convergent and optimal on the adaptively refined meshes generated by the newest vertex bisection algorithm. Numerical experiments are reported to confirm the theoretical analysis.

Shishun Li, Xinping Shao & Zhiyong Si. (2020). Local Multilevel Method on Adaptively Refined Meshes for Elliptic Problems with Smooth Complex Coefficients. Numerical Mathematics: Theory, Methods and Applications. 8 (3). 336-355. doi:10.4208/nmtma.2015.m1323
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