An optimal order $$H^{1}$$ -Galerkin mixed finite element method for good Boussinesq equation

IF 2.6 3区数学

Computational and Applied Mathematics Pub Date : 2024-09-10 DOI:10.1007/s40314-024-02914-0

L. Jones Tarcius Doss, V. Jenish Merlin

引用次数: 0

Abstract

In this paper, by introducing an intermediate function, a splitting technique is employed for the fourth order time dependent non-linear Good Boussinesq equation. Then, an $H^{1}$-Galerkin mixed finite element method is applied to the Good Boussinesq (GB) equation with cubic spline space as test and trial space in the method. This method may be considered as a Petrov-Galerkin method in which cubic splines are trial and linear splines (i.e second derivative of cubic splines)as test space. Optimal order error estimates are obtained for the both semi discrete scheme and fully discrete scheme. The Numerical illustration is presented to support the theoretical analysis.

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布西内斯克方程的最优阶 $$H^{1}$$ -Galerkin 混合有限元法

本文通过引入中间函数，对四阶时间相关非线性 Good Boussinesq 方程采用了分割技术。然后，将 $H^{1}$-Galerkin 混合有限元法应用于 Good Boussinesq (GB) 方程，并将三次样条空间作为该方法的测试和试验空间。该方法可视为一种 Petrov-Galerkin 方法，其中三次样条为试验空间，线性样条（即三次样条的二次导数）为测试空间。半离散方案和全离散方案均可获得最佳阶次误差估计值。为支持理论分析，还给出了数值说明。

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

Computational and Applied Mathematics MATHEMATICS, APPLIED-

自引率

11.50%

发文量

352

期刊介绍： Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.