The Crank-Nicolson weak Galerkin finite element methods for the sine-Gordon equation

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-01-29 DOI:10.1016/j.apnum.2025.01.016

Ahmed Al-Taweel , Jumana Alkhalissi , Xiaoshen Wang

引用次数: 0

Abstract

This article proposes an efficient second-order weak Galerkin (WG) finite element scheme for solving the 2D damped and undamped sine-Gordon problem with Dirichlet boundary conditions and initial conditions. We also construct and study a fully discrete WG finite element method for solving the sine-Gordon equation with a damping term using the Crank–Nicolson (CN) and Euler schemes. Stability and error analyses are established on a triangular grid for the constructed schemes in

L^{2}

and

H^{1}

norms for the fully discrete and semi-discrete formulation. Our formulation is accurate in space and time. Finally, numerical experiments are performed to validate the theoretical conclusions.

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.