Mathematical Sciences: Finite Element Methods for Partial Differential Equations

数学科学：偏微分方程的有限元方法

• 批准号: 8902120
• 负责人: Richard Falk
• 金额: $ 6.41万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902120&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Finite; Element; Methods

This project is concerned with the development and analysis of finite element methods for partial differential equations arising from mechanics. The topics of research include: (1) Investigation of the boundary layer of the Reissner-Mindlin plate model, including the development and rigorous justification of an asymptotic expansion of the solution in terms of appropriate powers of the plate thickness for boundary conditions modelling the "soft" simply supported and free plate. (2) The development of higher order uniformly accurate finite element methods for the Reissner-Mindlin model (generalizing a first order method previously developed). In addition, the boundary layer theory developed in (1) will be used to analyze the interior behavior of methods and to develop mesh refinement strategies for improved accuracy. (3) Investigation of the use of nonconforming finite elements for boundary value problems in elasticity. Particular attention is given to the validity of Korn's second inequality for nonconforming elements with traction boundary conditions and to determining the relationship of finite element methods based on equivalent formulations of the equations of linear elasticity. (4) Investigation of the use of nonconforming finite element methods for the approximation of first order linear scalar hyperbolic equations. One application is to the problem of identifying a variable coefficient in an elliptic partial differential equation.

该项目涉及力学偏微分方程的有限元方法的开发和分析。 研究主题包括：（1）Reissner-Mindlin 板模型边界层的研究，包括根据板厚度的适当幂对“软”简支和自由板进行边界条件建模的解决方案的渐近展开的开发和严格论证。 (2) Reissner-Mindlin 模型的高阶一致精确有限元方法的开发（概括了先前开发的一阶方法）。 此外，（1）中开发的边界层理论将用于分析方法的内部行为并开发网格细化策略以提高精度。 (3) 研究非相容有限元在弹性边值问题中的应用。 特别关注科恩第二不等式对于具有牵引边界条件的不相容单元的有效性，以及基于线弹性方程的等效公式来确定有限元方法的关系。 (4) 研究使用非协调有限元方法来逼近一阶线性标量双曲方程。 一种应用是解决椭圆偏微分方程中变量系数的识别问题。