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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.

作为对有限元法（FEM）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： 1．基于超圆方法的后验误差估计研究：对于泊松方程，我们用混合有限元及相关方法对上述后验方法进行了分析，并通过数值实验验证了结果。部分成果发表在国际期刊上。事实证明，本方法需要很少的误差常数，但其适用范围有限。我们还寻找其在更广泛的问题和不合格 FEM.2 中的有效性。插值误差常数的估计：我们分析了常数和符合线性三角形有限元中出现的各种插值误差常数。这些常数的定量评估对于后验误差估计和 Nakao 数值验证方法至关重要。结果发表在国际期刊上。我们还对非一致线性三角形进行了类似的分析。 3．电磁学 FEM 的开发和分析：与第 1 项和第 2 项相关，我们一直在研究电磁学 FEM。四边形单元的一些结果作为国际联合工作发表在国际期刊上。我们正在通过傅里叶有限元分析轴对称域上的麦克斯韦特征值问题。4。板弯曲有限元研究：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。我们现在正在研究横向剪力的确定方法。 5．间断伽辽金方法的研究：我们开始对间断伽辽金方法进行后验误差分析。第 2 项中的非一致性有限元法是此类方法的经典示例，并被视为我们研究的起点。