scholarly journals Numerical approximation of the generalized regularized long wave equation using Petrov–Galerkin finite element method

2019 ◽  
Vol 35 (6) ◽  
pp. 2236-2257 ◽  
Author(s):  
Samir Kumar Bhowmik ◽  
Seydi B. G. Karakoc
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equation ◽  
Numerical Approximation ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Element Method

scholarly journals A nodal discontinuous Galerkin finite element method for the poroelastic wave equation

2019 ◽  
Vol 23 (3) ◽  
pp. 595-615 ◽  
Author(s):  
Khemraj Shukla ◽  
Jan S. Hesthaven ◽  
José M. Carcione ◽  
Ruichao Ye ◽  
Josep de la Puente ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equation ◽  
Discontinuous Galerkin ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Discontinuous Galerkin Finite Element ◽  
Element Method

scholarly journals Boussinesq-Peregrine water wave models and their numerical approximation

2020 ◽  
Author(s):  
T Katsaounis ◽  
Dimitrios Mitsotakis ◽  
G Sadaka
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Approximation ◽  
Bottom Topography ◽  
Type Systems ◽  
Galerkin Finite Element Method ◽  
Convergence Properties ◽  
Galerkin Finite Element ◽  
New System ◽  
Element Method

© 2020 Elsevier Inc. In this paper we consider the numerical solution of Boussinesq-Peregrine type systems by the application of the Galerkin finite element method. The structure of the Boussinesq systems is explained and certain alternative nonlinear and dispersive terms are compared. A detailed study of the convergence properties of the standard Galerkin method, using various finite element spaces on unstructured triangular grids, is presented. Along with the study of the Peregrine system, a new Boussinesq system of BBM-BBM type is derived. The new system has the same structure in its momentum equation but differs slightly in the mass conservation equation compared to the Peregrine system. Further, the finite element method applied to the new system has better convergence properties, when used for its numerical approximation. Due to the lack of analytical formulas for solitary wave solutions for the systems under consideration, a Galerkin finite element method combined with the Petviashvili iteration is proposed for the numerical generation of accurate approximations of line solitary waves. Various numerical experiments related to the propagation of solitary and periodic waves over variable bottom topography and their interaction with the boundaries of the domains are presented. We conclude that both systems have similar accuracy when approximate long waves of small amplitude while the Galerkin finite element method is more efficient when applied to BBM-BBM type systems.

Discontinuous Galerkin Finite Element Method for the Wave Equation

2006 ◽  
Vol 44 (6) ◽  
pp. 2408-2431 ◽  
Author(s):  
Marcus J. Grote ◽  
Anna Schneebeli ◽  
Dominik Schötzau
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equation ◽  
Discontinuous Galerkin ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Discontinuous Galerkin Finite Element ◽  
Element Method

scholarly journals Boussinesq-Peregrine water wave models and their numerical approximation

2020 ◽  
Author(s):  
T Katsaounis ◽  
Dimitrios Mitsotakis ◽  
G Sadaka
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Approximation ◽  
Bottom Topography ◽  
Type Systems ◽  
Galerkin Finite Element Method ◽  
Convergence Properties ◽  
Galerkin Finite Element ◽  
New System ◽  
Element Method

© 2020 Elsevier Inc. In this paper we consider the numerical solution of Boussinesq-Peregrine type systems by the application of the Galerkin finite element method. The structure of the Boussinesq systems is explained and certain alternative nonlinear and dispersive terms are compared. A detailed study of the convergence properties of the standard Galerkin method, using various finite element spaces on unstructured triangular grids, is presented. Along with the study of the Peregrine system, a new Boussinesq system of BBM-BBM type is derived. The new system has the same structure in its momentum equation but differs slightly in the mass conservation equation compared to the Peregrine system. Further, the finite element method applied to the new system has better convergence properties, when used for its numerical approximation. Due to the lack of analytical formulas for solitary wave solutions for the systems under consideration, a Galerkin finite element method combined with the Petviashvili iteration is proposed for the numerical generation of accurate approximations of line solitary waves. Various numerical experiments related to the propagation of solitary and periodic waves over variable bottom topography and their interaction with the boundaries of the domains are presented. We conclude that both systems have similar accuracy when approximate long waves of small amplitude while the Galerkin finite element method is more efficient when applied to BBM-BBM type systems.

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