p-Dirichlet问题的Crouzeix-Raviart近似的误差分析

IF 3.8 2区数学 Q1 MATHEMATICS

Journal of Numerical Mathematics Pub Date : 2022-10-21 DOI:10.48550/arXiv.2210.12116

A. Kaltenbach

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引用次数: 4

摘要

在本文中，我们研究了对于某些p∈(1，∞)和δ大于或等于0具有(p， δ)结构的非线性偏微分方程的Crouzeix-Raviart近似。我们建立了先验误差估计，这对于所有p∈(1，∞)和δ小于或等于0是最优的，中等误差估计，即最佳近似结果，以及原始-对偶后验误差估计，这既可靠又有效。理论结果得到数值实验的支持。

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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Error analysis for a Crouzeix–Raviart approximation of the p-Dirichlet problem

Abstract In the present paper, we examine a Crouzeix–Raviart approximation for non-linear partial differential equations having a (p, δ)-structure for some p ∈ (1, ∞) and δ⩾0. We establish a priori error estimates, which are optimal for all p ∈ (1, ∞) and δ⩾0, medius error estimates, i.e., best-approximation results, and a primal-dual a posteriori error estimate, which is both reliable and efficient. The theoretical findings are supported by numerical experiments.

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来源期刊

Journal of Numerical Mathematics 数学-数学

CiteScore

5.90

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Numerical Mathematics (formerly East-West Journal of Numerical Mathematics) contains high-quality papers featuring contemporary research in all areas of Numerical Mathematics. This includes the development, analysis, and implementation of new and innovative methods in Numerical Linear Algebra, Numerical Analysis, Optimal Control/Optimization, and Scientific Computing. The journal will also publish applications-oriented papers with significant mathematical content in computational fluid dynamics and other areas of computational engineering, finance, and life sciences.