Implicit characteristic Galerkin method for convection-diffusion equations

This paper presents a characteristic Galerkin "nite element method with an implicit algorithm for solving multidimensional, time-dependent convection}di!usion equations. The method is formulated on the basis of the combination of both the precise and the implicit numerical integration procedures aiming to reference particles. The precise integration procedure with a 2N algorithm is taken as a tool to determine the material (Lagrangian) derivative of the convective function in the operator splitting procedure. The stability analysis of the algorithm and numerical results illustrate good performance of the present method in stability and accuracy.