Seminars on Numerical Algorithms, Analyses, and Applications：Improved adaptive two-grid method for nonsymmetric or indefinite elliptic problems

：钟柳强（华南师范大学）
：2023-06-23 11:00
：海韵园实验楼105报告厅

报告人：钟柳强（华南师范大学）

时  间：2023年6月23日11:00

地  点：海韵园实验楼105报告厅

内容摘要:

First, an improved adaptive two-grid method with a correction step is designed, which is characterized in that before constructing a symmetric positive definite discrete scheme, an additional symmetric positive definite residual equation needs to be solved, and the residual is updated to the finite element solution of the upper level grid. Secondly, a new residual-based posterior error indicator is constructed, and further by the reliability of the error indicator, the quasi-orthogonality of the energy norm error and the decaying property of the global posterior error indicator, we obtain the convergence of the improved adaptive two-grid method. Finally, corresponding numerical experiments are given to verify the effectiveness of the improved adaptive two-grid method. Compared with the existing adaptive two-grid method, experiments show that in some cases, for the same degree of freedom, the improved adaptive two-grid method has higher error accuracy, and is more robust to the coefficients of the model problem and the adaptive approach for the parameters.

个人简介：

钟柳强，华南师范大学数学科学学院三级教授、博士生导师。从事偏微分方程数值求解中的多水平法的设计分析、自适应有限元法理论及其应用。曾获得第14届国际数值分析--Leslie Fox奖、第14届美国多重网格法铜山会议论文竞赛奖和全国优秀博士学位论文。先后主持多项国家自然科学基金项目和多项省部级科研基金项目。在Math. Comp., SIAM J. Numer. Anal., Numer. Linear Algebra Appl., 中国科学-数学等国内外期刊发表系列论文。

 

联系人：陈黄鑫