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Dogan, Abdulkadir

A Galerkin finite element approach to Burgers’ equation. (English) Zbl 1054.65103

Appl. Math. Comput. 157, No. 2, 331-346 (2004).
Summary: A Galerkin finite element method is presented for the numerical solution of Burgers’ equation. A linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is found via a Crank-Nicolson approach involving a product approximation. It is shown that this method is capable of solving Burgers’ equation accurately for a wide range of viscosity values. The results show that the new method performs better than the most of the methods available in the literature.

Cited in 44 Documents

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)

Keywords:

Burgers’ equation; finite element methods; Galerkin finite element method; Crank-Nicolson method; numerical examples; comparison of methods
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\textit{A. Dogan}, Appl. Math. Comput. 157, No. 2, 331--346 (2004; Zbl 1054.65103)
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References:

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