Gardner, L. R. T.; Gardner, G. A.; Dogan, A. A Petrov-Galerkin finite element scheme for Burgers’ equation. (English) Zbl 0908.65089 Arab. J. Sci. Eng., Sect. C, Theme Issues 22, No. 2, 99-109 (1997). Summary: Burgers’ equation is solved by a Petrov-Galerkin method using quadratic B-spline spatial finite elements. A linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is obtained via a Crank-Nicolson approach involving a product approximation. Standard problems are solved to assess the properties of the algorithm. Cited in 11 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:Crank-Nicolson method; Burgers’ equation; Petrov-Galerkin method; quadratic B-spline spatial finite elements PDF BibTeX XML Cite \textit{L. R. T. Gardner} et al., Arab. J. Sci. Eng., Sect. C, Theme Issues 22, No. 2, 99--109 (1997; Zbl 0908.65089) OpenURL