Taylor-Galerkin method for advection-diffusion equation

Purpose - The purpose of this paper is to provide numerical solutions of the time-dependent advection-diffusion problem by using B-spline finite element methods in which Taylor series expansion is used for the related time discretization. Design/methodology/approach - The solution domain is partitioned into uniform mesh. The collocation and the Galerkin methods where B-spline functions are used as base functions are applied to advection-diffusion equation. Findings - Given methods are unconditionally stable and the obtained results are comparable with some earlier studies in terms of accuracy. Originality/value - Quadratic and cubic B-spline base functions are used with Taylor series expansion for the discretization of the equation.