Research Initiation Award: Superconvergence of Finite Element Approximations for the Second Order Elliptic Problems by L^2 Projection Methods

研究启动奖：L^2投影法对二阶椭圆问题有限元逼近的超收敛

• 批准号: 1505119
• 负责人: Anna Harris
• 金额: $ 18.73万
• 依托单位: University of Arkansas at Pine Bluff
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1505119&HistoricalAwards=false
• 关键词: Research; Initiation; Award; Superconvergence; Finite

Research Initiation Awards provide support for junior and mid-career faculty at Historically Black Colleges and Universities who are building new research programs or redirecting and rebuilding existing research programs. It is expected that the award helps to further the faculty member's research capability and effectiveness, improves research and teaching at her home institution, and involves undergraduate students in research experiences. The award to the University of Arkansas at Pine Bluff has potential broader impact in a number of areas. The project will focus on constructing a mathematical model on superconvergence of the nonconforming finite element method (NCFEM) for second-order elliptic problems by L-squared projection methods. This project will enhance the research experience and training of undergraduate students in mathematics at the institution. Additionally, a course in Finite Element Methods will be developed and offered as a topics course. The project will use L-squared projection methods to improve the convergence rate of an existing finite element solution so that the new approximation is closer to the exact solution than the existing finite element solution. The objectives are: to obtain mathematical theories for the superconvergence of NCFEM using various element spaces for the second order elliptic problems with the homogeneous essential Dirichlet and natural Neumann boundary conditions; to write computer programs to perform numerical approximations to support the theoretical results; and to investigate existing theoretical results for the superconvergence of the conforming finite element method for second-order elliptic problems by the L-squared projection method. Finally, mathematical theories will be tested with real world data for the Laplace and Poisson equations, which are used in modeling heat conduction, seepage through porous media, irrotational flow of ideal fluids, and other applications.

研究启动奖为传统黑人学院和大学的初级和中期职业教师提供支持，他们正在建立新的研究项目或重新指导和重建现有的研究项目。期望该奖项有助于进一步提高教师的研究能力和效率，改善其所在机构的研究和教学，并使本科生参与研究经验。该奖项授予派恩布拉夫的阿肯色大学，可能在许多领域产生更广泛的影响。本课题主要研究用l平方投影法建立二阶椭圆问题非协调有限元法超收敛的数学模型。此计划将提升本校数学专业本科生的研究经验及训练。此外，将开发一门有限元方法课程，并作为主题课程提供。该项目将使用l平方投影方法来提高现有有限元解的收敛速度，以便新的近似比现有的有限元解更接近精确解。目的是：得到具有齐次本质Dirichlet和自然Neumann边界条件的二阶椭圆型问题的NCFEM在各种元空间下的超收敛性的数学理论；编写计算机程序进行数值近似，以支持理论结果；利用l平方投影法研究二阶椭圆型问题的一致性有限元法的超收敛性的现有理论结果。最后，数学理论将用拉普拉斯和泊松方程的真实世界数据进行测试，这些方程用于模拟热传导，多孔介质的渗透，理想流体的无旋流以及其他应用。

项目成果

Numerical Experiments Using MATLAB: Superconvergence of Conforming Finite, Element Approximation for Second Order, Elliptic Problems

使用 MATLAB 进行数值实验：二阶椭圆问题的符合有限元逼近的超收敛

• DOI: 10.4236/am.2018.96047
• 发表时间: 2018
• 期刊: Applied Mathematics
• 作者: Harris, Anna;Harris, Stephen;Gardner, Camille;Brock, Tyrone
• 通讯作者: Brock, Tyrone

QoS Parametric Inspection of Uniform and Assorted Trajectories for MANET Routing Protocols

MANET 路由协议的统一和分类轨迹的 QoS 参数检查

• DOI: 10.4236/ijcns.2017.1010014
• 发表时间: 2017
• 期刊: Network and System Sciences
• 作者: Sehwani, Nitesh;Rahman, Sajid;Harris, Anna
• 通讯作者: Harris, Anna

Numerical Experiments Using MATLAB: Superconvergence of Nonconforming Finite Element Approximation for Second-Order Elliptic Problems

使用 MATLAB 的数值实验：二阶椭圆问题的非一致有限元逼近的超收敛

• DOI: 10.4236/am.2016.717173
• 发表时间: 2016
• 期刊: Applied Mathematics
• 作者: Harris, Anna;Harris, Stephen;Rauls, Danielle
• 通讯作者: Rauls, Danielle