How to recover the gradient of linear elements on nonuniform triangulations

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics Pub Date : 1996-01-01 DOI:10.21136/am.1996.134325

I. Hlavácek, M. Křížek, Vladislav Pištora

引用次数: 26

Abstract

We propose and examine a simple averaging formula for the gradient of linear finite elements in $R^d$ whose interpolation order in the $L^q$-norm is $\mathcal O(h^2)$ for $d<2q$ and nonuniform triangulations. For elliptic problems in $R^2$ we derive an interior superconvergence for the averaged gradient over quasiuniform triangulations. A numerical example is presented.

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如何恢复非均匀三角形上线性元素的梯度

我们提出并检验了线性有限元在$R^d$中梯度的一个简单的平均公式，其在$L^q$范数中的插值阶为$\mathcal O(h^2)$，对于$d<2q$和非均匀三角剖分。对于$R^2$中的椭圆型问题，我们导出了拟均匀三角形上平均梯度的内超收敛性。给出了一个数值算例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applications of Mathematics 数学-应用数学

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Applications of Mathematics publishes original high quality research papers that are directed towards applications of mathematical methods in various branches of science and engineering. The main topics covered include: - Mechanics of Solids; - Fluid Mechanics; - Electrical Engineering; - Solutions of Differential and Integral Equations; - Mathematical Physics; - Optimization; - Probability Mathematical Statistics. The journal is of interest to a wide audience of mathematicians, scientists and engineers concerned with the development of scientific computing, mathematical statistics and applicable mathematics in general.