Galerkin-least square B-spline approach toward advection–diffusion equation

Dhawan, Sharanjeet; Bhowmik, Samir Kumar; Kumar, Sudhir

doi:10.1016/j.amc.2015.03.092

Cited by 9 publications

(4 citation statements)

References 16 publications

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“…ADE is also handled by means of the least squares method. A space time least-squares finite elements scheme is constructed for advection-diffusion equation [11], space-time Galerkin least squares method for the one-dimensional ADE is proposed in the works [12,13]. The space time least squares method was set up by way of both linear and quadratic B-spline shape functions for computing numerical solutions of the ADE [14].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions of Advection-Diffusion Equation via Quartic B-Spline Least Squares Method

AY,

SAKA,

ERSOY HEPSON

et al. 2023

Eskişehir Türk Dünyası Uygulama Ve Araştırma Merkezi Bilişim Dergisi

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En küçük Kareler metodu (LSM) kullanılarak zamana bağlı bir boyutlu Advection-Diffusion denklemi (ADE) için yaklaşık çözümler elde edilmiştir..LSM de deneme fonksiyonu olarak kuartic B-spline fonksiyonların kombinasyonu kullanılmıştır. Bilinmeyenlerine deneme fonksiyonu tanımlanmış karesi alınmış ADE ‘nin integralinin deneme fonksiyonun zaman parametresine göre türevi alınarak ağırlık fonksiyonu belirlenmiştir. Metodun başarısı üç test problem çalışılarak gösterilmiştir.

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Section: Introductionmentioning

confidence: 99%

Numerical Solutions of Advection-Diffusion Equation via Quartic B-Spline Least Squares Method

AY,

SAKA,

ERSOY HEPSON

et al. 2023

Eskişehir Türk Dünyası Uygulama Ve Araştırma Merkezi Bilişim Dergisi

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“…In the finite element method, the unknown function of differential equations and its derivatives over each elements is represented as linear combination of both undetermined time parameters and spline functions. The B‐splines are popularly applied in solving the differential equations [2, 5–7, 11, 12]. To beat the limitation of the B‐splines especially for constructing curve and surfaces discussed in [22], useful nonpolynomial B‐splines, such as exponential B‐splines, trigonometric B‐splines, hyperbolic B‐splines and etc.…”

Section: Introductionmentioning

confidence: 99%

A quartic trigonometric tension B‐spline finite element method for solving Gardner equation

Hepson

2022

Numerical Methods Partial

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The collocation method is established for getting solution of the Gardner equation (GE). The GE is fully integrated by way of the Crank-Nicolson method for time variable and collocation method for spatial variable. Trial function of the collocation method is set up using combination of quartic trigonometric tension (QTT) B-splines. Convergence analysis of suggested method is investigated. Performance of the QTT B-splines is searched by studying three test problems: propagation of bell shape solitary wave, interaction of two positive bell shape solitary wave and wave generation.

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“…The use of various degrees of B-spline functions to obtain the numerical solutions of some PDEs has been shown to provide easy and simple algorithms. For instance, B-spline finite elements have been widely applied to solve elliptic equations [ 14 , 15 ], Korteweg-De Vries equation [ 16 – 18 ], Burgers’ equation [ 19 – 22 ], regularized long-wave equation [ 23 , 24 ], Fokker-Planck equation [ 25 ], advection-diffusion equation [ 26 ], and generalized equal width wave equation [ 27 ], etc., successfully. However, to the best knowledge of the authors, the B-spline FEM method is not considered for finding the approximate solution of the diffusion equation with delay.…”

Section: Introductionmentioning

confidence: 99%

Linear B-spline finite element method for the generalized diffusion equation with delay

Lubo

Duressa

2022

BMC Res Notes

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Objectives The main aim of this paper is to develop a linear B-spline finite element method for solving generalized diffusion equations with delay. The linear B-spline basis function is used to discretize the space variable. The time discretization process is based on Crank-Nicolson. The benefit of the scheme is that the numerical solution is obtained as a smooth piecewise continuous function which empowers one to find an approximate solution at any desired position in the domain. Result Sufficient and necessary conditions for the numerical method to be asymptotically stable are derived. The convergence of the numerical method is studied. Some numerical experiments are performed to verify the applicability of the numerical method.

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Galerkin-least square B-spline approach toward advection–diffusion equation

Cited by 9 publications

References 16 publications

Numerical Solutions of Advection-Diffusion Equation via Quartic B-Spline Least Squares Method

Numerical Solutions of Advection-Diffusion Equation via Quartic B-Spline Least Squares Method

A quartic trigonometric tension B‐spline finite element method for solving Gardner equation

Linear B-spline finite element method for the generalized diffusion equation with delay

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