Finite Element Superconvergence in Computational Mechanics

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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.