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Study of methodology for a posterior error estimation of finite element solutions

有限元解后验误差估计方法的研究

基本信息

批准号：
16540096
负责人：
KIKUCHI Fumio
金额：
$ 1.6万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540096/
关键词：
numerical analysis finite element method a posteriori error estimate hypercircle method interpolation error constant verification of accuracy mixed and non-conforming methods numerical experiment 混合法誤差定数

项目摘要

As a study of methods and techniques for a posteriori error estimation of the finite element method (FEM), we obtained the following results and observations.1. Study of a posteriori error estimation based on the hypercircle method : For Poisson's equation, we have analyzed the above a posteriori method with the mixed FEM and related methods, and verified the results by numerical experiment. Some results were published in an international journal. The present method turns out to require very few error constants but its range of applicability is limited. We also search for its effectiveness in wider problems and non-conforming FEM.2. Estimation of interpolation error constants : We analyzed various interpolation error constants appearing in the constant and conforming linear triangular finite elements. Quantitative evaluation of such constants is essential in a posteriori error estimation and Nakao's numerical verification method. The results were published in international journals. We also perform similar analysis for the non-conforming linear triangle.3. Development and analysis of FEM for electromagnetics : Related to items 1 and 2, we have been studying FEM for electromagnetics. Some results for quadrilateral elements were published in an international journal as an international joint work. We are analyzing Maxwell's eigenvalue problems over axisymmetric domains by the Fourier FEM.4. Study of plate bending FEM : We have studied and published a unification method for the Kirchhoff and Reissner-Mindlin elements in an international journal. We are now studying determination method for the transverse shear forces.5. Study of the discontinuous Galerkin method : We start a posteriori error analysis of the discontinuous Galerkin method. The non-conforming FEM in item 2 is a classical example of such method, and is taken as a starting point of our study.

作为有限元后验误差估计方法和技术的研究，我们得到了以下结果和观察.基于超圆方法的后验误差估计研究：对于Poisson方程，我们用混合有限元法及相关方法对上述后验误差估计方法进行了分析，并通过数值实验对结果进行了验证。一些研究结果发表在一份国际期刊上。目前的方法原来需要很少的误差常数，但其适用范围是有限的。我们还寻找它的有效性，在更广泛的问题和不符合有限元。插值误差常数的估计：分析了常值线性三角形单元和协调线性三角形单元中出现的各种插值误差常数。定量评估这些常数是必不可少的后验误差估计和Nakao的数值验证方法。研究结果发表在国际期刊上。对非协调线性三角形也进行了类似的分析.电磁场有限元法的开发与分析：与第1项和第2项相关，我们一直在研究电磁场有限元法。四边形单元的一些结果作为国际合作成果发表在国际期刊上。我们用傅里叶有限元法分析轴对称区域上的麦克斯韦本征值问题.板弯曲有限元的研究：我们研究了Kirchhoff和Reissner-Mindlin单元的统一方法，并在国际期刊上发表。我们正在研究横向剪力的确定方法.间断Galerkin方法的研究：我们开始间断Galerkin方法的后验误差分析。第2项中的非协调有限元法是这种方法的一个经典例子，并作为我们研究的起点。