Optimal convergence rates in L² for a first order system least squares finite element method

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2023-01-01 DOI:10.1051/m2an/2022026

Maximilian Bernkopf, Jens Markus Melenk

引用次数: 0

Abstract

We analyze a divergence based first order system least squares method applied to a second order elliptic model problem with homogeneous boundary conditions. We prove optimal convergence in the L 2 (Ω) norm for the scalar variable. Numerical results confirm our findings.

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一阶系统最小二乘有限元法在L2中的最优收敛率

分析了一阶系统最小二乘法在二阶齐次边界条件椭圆模型问题上的应用。我们证明了标量变量在l2 (Ω)范数上的最优收敛性。数值结果证实了我们的发现。

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

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.

Optimal convergence rates in L2 for a first order system least squares finite element method

Abstract

Optimal convergence rates in L² for a first order system least squares finite element method