A novel post-processed finite element method and its convergence for partial differential equations

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-10-22 DOI:10.1016/j.cam.2024.116319

Wenming He , Jiming Wu , Zhimin Zhang

引用次数: 0

Abstract

In this article, by combining high-order interpolation on coarse meshes and low-order finite element solutions on fine meshes, we propose a novel approach to improve the accuracy of the finite element method. The new method is in general suitable for most partial differential equations. For simplicity, we use the second-order elliptic problem as an example to show how the novel approach improves the accuracy of the finite element method. Numerical tests are also conducted to validate the main theoretical results.

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新颖的后处理有限元方法及其对偏微分方程的收敛性

本文结合粗网格上的高阶插值和细网格上的低阶有限元求解，提出了一种提高有限元方法精度的新方法。新方法一般适用于大多数偏微分方程。为简单起见，我们以二阶椭圆问题为例，说明新方法如何提高有限元方法的精度。我们还进行了数值测试，以验证主要理论结果。

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

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.