| Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems |
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| 作者姓名： | WU Haijun & CHEN Zhiming Institute of Computational Mathematics Chinese Academy of Sciences Beijing China. |
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| 作者单位： | WU Haijun & CHEN Zhiming Institute of Computational Mathematics，Chinese Academy of Sciences，Beijing 100080，China. Department of Mathematics，Nanjing University，Nanjing 210093，China |
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| 基金项目： | 国家自然科学基金;国家重点基础研究发展计划(973计划);国家自然科学基金;监察部资助项目 |
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| 摘 要： | In this paper we prove the uniform convergence of the standard multigrid V-cycle algorithm with the Gauss-Seidel relaxation performed only on the new nodes and their "immediate" neighbors for discrete elliptic problems on the adaptively refined finite element meshes using the newest vertex bisection algorithm. The proof depends on sharp estimates on the relationship of local mesh sizes and a new stability estimate for the space decomposition based on the Scott-Zhang interpolation operator. Extensive numerical results are reported, which confirm the theoretical analysis.
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| 收稿时间： | 2 August 2005 |
| 修稿时间： | 24 March 2006 |
Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems |
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| WU Haijun & CHEN Zhiming Institute of Computational Mathematics,Chinese Academy of Sciences,Beijing ,China..Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems[J].Science in China(Mathematics),2006,49(10):1405-1429. |
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| Authors: | WU Haijun CHEN Zhiming |
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| Institution: | 1. Department of Mathematics, Nanjing University, Nanjing 210093, China
2. Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China. |
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| Abstract: | In this paper we prove the uniform convergence of the standard multigrid V-cycle algorithm with the Gauss-Seidel relaxation performed only on the new nodes and their "immediate" neighbors for discrete elliptic problems on the adaptively refined finite element meshes using the newest vertex bisection algorithm. The proof depends on sharp estimates on the relationship of local mesh sizes and a new stability estimate for the space decomposition based on the Scott-Zhang interpolation operator. Extensive numerical results are reported, which confirm the theoretical analysis. |
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| Keywords: | Multigrid V-cycle algorithm adaptive finite element meshes local relaxation Scott-Zhang interpolation |
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