Superconvergence of p-version/spectral collocation, discontinuous Galerkin methods and eigenvalue approximation

p版本/谱搭配的超收敛、不连续伽辽金方法和特征值近似

• 批准号: 0612908
• 负责人: Zhimin Zhang
• 金额: $ 20万
• 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: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0612908&HistoricalAwards=false
• 关键词: Superconvergence; version; spectral; collocation; discontinuous

The investigator and his colleagues study the superconvergence phenomenon and its recovery of several major computational methods in science and engineering. The research objectives include (1) to develop a superconvergence recovery technique and associated errorestimator for discontinuous Galerkin method; (2) to enhance the eigenvalue approximation by recovery techniques; and (3) to investigate superconvergence phenomena of p-version/spectral collocation methods. Some recent mathematical theory in finite element superconvergence, discontinuous Galerkin methods, as well as domain variation techniques in the PDE theory and classical results in approximation theory will be employed in the project.The study is of great importance for the adaptive design ofcomputational algorithms and has a direct application inengineering computation. The success of the project will bridge a gap between engineering practice and mathematical theoretical development and widen the knowledge in the scientific community. The project has solid multi- and interdisciplinary contents and wide application in the software industry.

研究者及其同事研究了超融合现象及其在科学与工程学中的几种主要计算方法的恢复。研究目标包括（1）以开发不连续的盖尔金方法的超对流恢复技术和相关的错误估计器； （2）通过恢复技术增强特征值近似； （3）研究p version/频谱搭配方法的超授权现象。项目中将采用一些最新的数学理论，这些数学元素超级范围，不连续的Galerkin方法以及PDE理论中的域变化技术，并且在项目中将采用近似理论的经典结果。该研究对于自适应设计算法和直接应用程序的自适应设计非常重要。该项目的成功将弥合工程实践与数学理论发展之间的差距，并扩大科学界的知识。该项目在软件行业中具有扎实的多学科内容和广泛的应用。