The finite volume element (FVE) methods used currently are essentially low order and unsymmetric. In this paper, by biquadratic elements and multistep methods, we construct a second order FVE scheme for nonlinear convection diffusion problem on nonuniform rectangular meshes. To overcome the numerical oscillation, we discretize the problem along its characteristic direction. The choice of alternating direction strategy is critical in this paper, which guarantees the high efficiency and symmetry of the discrete scheme. Optimal order error estimates in H1-norm are derived and a numerical example is given at the end to confirm the usefulness of the method. © 2006 Elsevier B.V. All rights reserved.
Yang, M., & Yuan, Y. (2007). A symmetric characteristic FVE method with second order accuracy for nonlinear convection diffusion problems. Journal of Computational and Applied Mathematics, 200(2), 677–700. https://doi.org/10.1016/j.cam.2006.01.020