Taylor‐Galerkin method for advection‐diffusion equation

Abstract

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.