A Robust Method for the Numerical Solution of the Advection-Diffusion Equation Using the Galerkin Method Based on Hermite B-Spline Functions

Öz

The goal of this research is to find an approximate solution to the one-dimensional linear advection-diffusion equation using the cubic Hermite B-Spline Galerkin finite element method, a new numerical method developed by selecting cubic Hermite B-spline functions as the basis functions. After discretizing the advection-diffusion equation in the temporal direction using the Crank-Nicolson formula, the spatial discretization of the semi-discrete scheme was performed using cubic Hermite B-spline functions. The effectiveness and accuracy of the proposed method were tested using the four most well-known model problems in the literature. The obtained numerical results were compared with those of other studies in the literature and presented in tabular form. Additionally, to observe the agreement of the approximate solutions with the analytical solution of the model problems, the graphs of the analytical and the approximate solutions were plotted together, and the graphs of the absolute error were plotted.

Anahtar Kelimeler

• Galerkin method
• Advection-diffusion equation
• Hermite B-spline function
• Finite element method
• Legendre polynomials

Etik Beyan

Ethics committee approval was not required for this study because of there was no study on animals or humans.

Kaynakça

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