A Lagrange Galerkin Scheme for the Numerical Stability of the Shallow Water Equations with the Transmission Boundary Condition through Energy Estimates

Md. Masum Murshed *

Department of Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh.
 
Research Article
World Journal of Advanced Engineering Technology and Sciences, 2024, 12(02), 832–840.
Article DOI: 10.30574/wjaets.2024.12.2.0350
Publication history: 
Received on 09 July 2024; revised on 15 August 2024; accepted on 17 August 2024
 
Abstract: 
This paper presents a study on the shallow water equations (SWEs) with specified Dirichlet and transmission boundary conditions (TBC). A Lagrange-Galerkin (LG) scheme is employed for numerical discretization. The stability of the solution is analyzed using energy estimates. The results shows that the total energy generally decreases over time and that the energy derivatives are non-positive, which confirms the numerical stability of the solution.
 
Keywords: 
Lagrange Galerkin Scheme; Numerical Stability; Shallow Water Equations; Transmission Boundary Condition; Energy Estimates
 
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