Finite Element Superconvergence in Computational Mechanics

计算力学中的有限元超收敛

• 批准号: 0074301
• 负责人: Zhimin Zhang
• 金额: $ 10万
• 依托单位: Wayne State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-15 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0074301&HistoricalAwards=false
• 关键词: Finite; Element; Superconvergence; Computational; Mechanics

Proposal Title: Finite Element Superconvergence in Computational MechanicsProposal ID Number: DMS-0074301AbstractThe objective of this project is the finite element superconvergence. The research efforts will be devoted (1) to develop general theory of finite element superconvergence and its recovery with emphases on triangular elements, irregular grids, and harmonic functions; (2) to develop superconvergent theory for those successful numerical methods in handling boundary layers and locking. Some recent mathematical theory in finite element superconvergence, asymptotic regularity, as well as improved interior analysis will be employed in the roject.The superconvergence study is of great importance for adaptive design of computational algorithms. Therefore, the proposed research has a direct application in high-performance computing, computational mechanics, computational fluid dynamics, financial mathematics, mathematical biology, manufacturing, and other scientific fields. The research will widen the knowledge in scientific community on both mathematical theory and practical algorithm design.

提案标题：计算力学中的有限元超收敛问题。 研究工作将致力于（1）发展有限元超收敛及其恢复的一般理论，重点是三角形单元，不规则网格和调和函数;（2）发展超收敛理论，为那些成功的数值方法处理边界层和锁定。 本课题将利用有限元超收敛、渐近正则性以及改进的内点分析等数学理论，研究有限元超收敛问题对于自适应设计计算算法具有重要意义。 因此，本文的研究在高性能计算、计算力学、计算流体力学、金融数学、数学生物学、制造业等科学领域有着直接的应用。 该研究将拓宽科学界在数学理论和实际算法设计方面的知识。