| 基于几何质量和后验误差的网格优化设计 |
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| 引用本文： | 宣兆成.基于几何质量和后验误差的网格优化设计[J].天津工程师范学院学报,2005,15(4):1-7,13. |
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| 作者姓名： | 宣兆成 |
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| 作者单位： | 天津工程师范学院,计算机系,天津,300222 |
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| 基金项目： | 天津市应用基础研究计划项目（05YFJMJC13300） |
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| 摘 要： | 给出了偏微分方程的h型有限元分析的双层网格最优精化设计方法。第一层是细化后验误差相对大的单元？后验误差是通过简化计算由单元平均流量为连接的单元Neumann型子问题而得到的误差界。简化计算就是只把由1／2单元尺寸所构成的网格上的泛函作为单元残余误差方程的试探函数，这样计算成本将非常小。某些精化后的网格的几何性质将变得很差，所以第二层又用Laplace光顺算法对网格的质量进行改进，并用两个例题验证了该方法。结果表明，算法达到最优收敛率，并提高了精度。
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| 关 键 词： | 网格 误差 几何 精化 |
| 文章编号： | 1673-1018（2005）04-0000-07 |
| 收稿时间： | 11 1 2005 12:00AM |
| 修稿时间： | 2005-11-01 |
Optimal mesh refinement based on a-posteriori error estimator and geometrical quality |
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| XUAN Zhao-cheng.Optimal mesh refinement based on a-posteriori error estimator and geometrical quality[J].Journal of Tianji University of Technology and Education,2005,15(4):1-7,13. |
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| Authors: | XUAN Zhao-cheng |
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| Institution: | Department of Computer Science, Tianjin University of Technology and Education, Tianjin 300222, China |
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| Abstract: | A two-level optimal mesh refinement method for h-version finite element analysis of partial differential equations is presented based on both a-posteriori error indicator and geometrical quality of mesh. The first level is to refine the meshes on which the a-posteriori error indicators are relatively higher than the others. The error indicators are obtained by simplifying computation of the error bounds which are obtained by solving elemental Neumann type subproblems with the averaged flux for the consistency of the Neumann problems. The simplification of computation means that the functional space on the mesh uniformly refined with only half size of the coarse mesh is chosen as the test functional space in the elemental residual form of error equations, thus the cost of computing the error indicators will be very low, After refinement, some refined triangles will become poorly shaped or distorted, then the second level is to move the meshes to improve their geometrical quality with Laplacian smoothing algorithm. Two examples are computed to verify this method and the results show that the refined mesh obtained by both the a-posteriori error indicator and mesh smoothing gives the optimal convergence and more accuracy for the results. |
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| Keywords: | mesh error geometry refinement |
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