A finite element method for extended KdV equations

Anna Karczewska; Piotr Rozmej; Maciej Szczeciński; Bartosz Boguniewicz

International Journal of Applied Mathematics and Computer Science (2016)

  • Volume: 26, Issue: 3, page 555-567
  • ISSN: 1641-876X

Abstract

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The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.

How to cite

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Anna Karczewska, et al. "A finite element method for extended KdV equations." International Journal of Applied Mathematics and Computer Science 26.3 (2016): 555-567. <http://eudml.org/doc/286722>.

@article{AnnaKarczewska2016,
abstract = {The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.},
author = {Anna Karczewska, Piotr Rozmej, Maciej Szczeciński, Bartosz Boguniewicz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {shallow water wave problem; nonlinear equations; second order KdV equations; finite element method; Petrov-Galerkin method},
language = {eng},
number = {3},
pages = {555-567},
title = {A finite element method for extended KdV equations},
url = {http://eudml.org/doc/286722},
volume = {26},
year = {2016},
}

TY - JOUR
AU - Anna Karczewska
AU - Piotr Rozmej
AU - Maciej Szczeciński
AU - Bartosz Boguniewicz
TI - A finite element method for extended KdV equations
JO - International Journal of Applied Mathematics and Computer Science
PY - 2016
VL - 26
IS - 3
SP - 555
EP - 567
AB - The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.
LA - eng
KW - shallow water wave problem; nonlinear equations; second order KdV equations; finite element method; Petrov-Galerkin method
UR - http://eudml.org/doc/286722
ER -

References

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