Analytical and Rothe time-discretization method for a Boussinesq-type system over an uneven bottom
type: Item
instance of: scholarly article
title: Analytical and Rothe time-discretization method for a Boussinesq-type system over an uneven bottom
zbMATH Open document ID: 1472.65113
author: Luis Fernando Mejía
author: Juan C. Muñoz
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2021-08-16T00:00:00Z
review text: The authors consider the analytical and numerical resolution of a 2D version of a Boussinesq-type model which occur in the water wave propagation. The time discretization is performed using a finite-difference second-order Crank-Nicholson-type scheme, and then, at each time step, the spatial variables are discretized with an efficient Galerkin/Finite Element Method (FEM) using triangular-finite elements based on 2D piecewise-linear Lagrange interpolation. Some numerical tests are presented to support the theoretical results.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65M22
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 76B25
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 7382139
zbMATH Keywords: Boussinesq-type system
zbMATH Keywords: moving bathymetry
zbMATH Keywords: finite element method
zbMATH Keywords: Crank-Nicholson-type scheme
describes a project that uses: Gmsh
describes a project that uses: FEniCS
MaRDI profile type: Publication
full work available at URL: j.cnsns.2021.105951
OpenAlex ID: W3177557335
cites work: Long waves on a beach
cites work: A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves
cites work: Numerical investigation of a two-dimensional Boussinesq system
cites work: Equations for bi-directional waves over an uneven bottom
cites work: On the Galerkin/finite-element method for the Serre equations
cites work: On some Boussinesq systems in two space dimensions: theory and numerical analysis
cites work: On initial-boundary value problems for a Boussinesq system of BBM-BBM type in a plane domain
cites work: Galerkin finite element solution for Benjamin-Bona-Mahony-Burgers equation with cubic B-splines
cites work: Solution of 2D Boussinesq systems with freefem++: the flat bottom case
cites work: Boussinesq systems of Bona-Smith type on plane domains: theory and numerical analysis
cites work: Boussinesq systems in two space dimensions over a variable bottom for the generation and propagation of tsunami waves
cites work: Boussinesq-type equations with improved nonlinear performance
cites work: A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics
cites work: Dispersive Shallow Water Wave Modelling. Part I: Model Derivation on a Globally Flat Space
cites work: A finite element method for the two-dimensional extended Boussinesq equations
cites work: Q5189317
cites work: Elliptic Differential Equations
cites work: Q4100575
cites work: Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
cites work: The finite element methods for elliptic problems.
cites work: Q4663944
cites work: A three-dimensional Dirichlet-to-Neumann operator for water waves over topography
cites work: Generation of upstream advancing solitons by moving disturbances
cites work: Water waves generated by a moving bottom
cites work: A non-hydrostatic numerical scheme for dispersive waves generated by bottom motion
cites work: A note on tsunamis: their generation and propagation in an ocean of uniform depth
cites work: The Korteweg-de Vries equation and water waves. Part 2. Comparison with experiments
cites work: The Korteweg-de Vries equation and water waves. Part 3. Oscillatory waves
cites work: Comparison between three-dimensional linear and nonlinear tsunami generation models
DOI: 10.1016/J.CNSNS.2021.105951
description: scientific article; zbMATH DE number 7382139