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Numerical solutions of Boussinesq equation using Galerkin finite element method
Author(s) -
Ucar Yusuf,
Esen Alaattin,
Karaagac Berat
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22600
Subject(s) - mathematics , boussinesq approximation (buoyancy) , galerkin method , finite element method , mathematical analysis , discontinuous galerkin method , basis function , petrov–galerkin method , extended finite element method , numerical analysis , mechanics , physics , natural convection , rayleigh number , convection , thermodynamics
In this study, Galerkin finite element method has been applied to good Boussinesq (GBq) and bad Boussinesq (BBq) equations which are examples of Boussinesq type equations. To apply the method, cubic B‐spline basis functions are taken as element and weight functions. The solutions of the numerical schemes have been obtained using the fourth order Runge–Kutta method. The error norms L 2 and L ∞ have been used to test how compatible they obtained numerical solutions with those of exact ones. As numerical examples, solitary wave motion and interaction of solitary waves have been investigated for both GBq and BBq equation. Also blow‐up solutions related to the interaction of two solitary waves are considered for GBq equation.