Synthetic approach for the development of computer assisted analysis from the numerical verification methods

从数值验证方法发展计算机辅助分析的综合方法

基本信息

批准号：
15204007
负责人：
NAKAO Mitsuhiro
金额：
$ 20.63万
依托单位：
KYUSHU UNIVERCITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2006
项目状态：
已结题

项目摘要

In this research, we newly developed the numerical verification methods which can be applied to wide mathematical and analytical problems, as well as extended or improved the existing techniques.And we actually applied these methods to particular problems such as equations in the mathematical fluid mechanics and oscillation problems etc. The important research results obtained by investigators and co-investigators are as follows :1.Nakao, N.Yamamoto, Watanabe established several refinements and extensions for the constructive error estimates for the finite finite element projections of the Poisson and the bi-harmonic equations on various kinds of domains, particularly, on nonconvex polygonal domains. These results played important and essential roles for the numerical verification of solutions of nonlinear elliptic equations and the two dimensional stationary Navier-Stokes problems.2.Nagatou numerically proved the stability of the flow on the torus called Kolmogorov problem.3.Minamoto presented a formulation of the verification condition for the double turning point and applied it to the perturbed Gelfand equation.4.Oishi established some refinements on the fast algorithm for the solutions of linear equations.5.Nishida et al. presented the computed results with guaranteed error bounds for the symmetry breaking bifurcation point of the solution of two dimensional heat convection problems, as well as they formulated the numerical verification algorithm for the three dimensional problems with some prototypical verified examples.6.Chin obtained some numerical verification results on the existence of solutions and a posteriori error estimates for the linear complementarity problems.

In this research, we newly developed the numerical verification methods which can be applied to wide mathematical and analytical problems, as well as extended or improved the existing techniques.And we actually applied these methods to particular problems such as equations in the mathematical fluid mechanics and oscillation problems etc. The important research results obtained by investigators and co-investigators are as follows :1.Nakao, N.Yamamoto, Watanabe established several对泊松的有限元预测的建设性误差估计的细化和扩展，以及各种域上的双谐波方程，尤其是在非凸多边形域上。这些结果在数值验证非线性椭圆方程和二维固定的Navier-Stokes问题的数值验证方面起着重要而重要的作用。2.Nagatou在数值上证明了流动在摩尔莫戈罗夫问题上的流量稳定性。3.Minamoto提出了验证的验证条件的验证，并在poupterifor point offiend point point和offied offied point offied point和off offied toper。线性方程溶液的快速算法的改进。5.Nishida等。介绍了在两个维热对流问题解决方案的对称性破坏分叉点具有保证的误差界限的计算结果，并且它们制定了三维问题的数值验证算法，具有一些原型验证的示例。6.CHIN获得了解决方案的数字验证，以解决方案和pocteri erseri referi referi sorieri soriori eriori referie seriori seriori erecter seriori erecter seriori估计。