Mathematical Sciences and Computer Research: Higher Order Finite Element Methods and Adaptive Approaches

研究者和他的同事们继续研究和发展高精度的有限元方法来计算偏微分方程的解。他们在之前的工作中已经表明，高阶方法，如hp版本的有限元方法，是非常有效的。最近，这些方法已在各种工程项目（包括商业）中实施。主要研究具有重要工程应用价值的固体力学问题的数学和数值问题，如三维体的断裂、板壳的建模等。研究的目标是建立数学结果，将用于工程问题的计算机分析。这些结果将允许开发高效的计算方法，用于广泛应用于工程科学和实践的研究和商业计算机代码。

The investigator and his colleagues continue their study and development of highly accurate finite element methods for computing solutions of partial differential equations. They have shown in previous work that high degree methods, such as the h-p version of the finite element method, are very effective. Recently these methods have been implemented in various engineering programs (inclusive of commercial). The research will concentrate on mathematical and numerical problems leading to the reliable solution of problems of solid mechanics with important applications in engineering, such as fractures in 3- dimensional bodies, modelling of plates and shells, etc. The goal of the research is to establish mathematical results that will be used in the computer analysis of engineering problems. These results will allow to be developed highly effective computational methods for broad applications in research and commercial computer codes that are widely used in engineering science and practice.