Finite Element Superconvergence in Computational Mechanics

提案标题：计算力学中的有限元超收敛建议ID号：DMS-0074301本项目的目标是有限元超收敛。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)为那些在处理边界层和锁定方面取得成功的数值方法发展超收敛理论。利用有限元超收敛、渐近正则性以及改进的内点分析等最新的数学理论，研究超收敛问题对计算算法的自适应设计具有重要意义。因此，该研究在高性能计算、计算力学、计算流体力学、金融数学、数学生物学、制造业等科学领域具有直接的应用价值。这项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。

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.