Entropy Schemes for One-Dimensional Convection-Diffusion Equations

In this paper, we extend the entropy scheme for hyperbolic conservation laws to one-dimensional convection-diffusion equation. The operator splitting method is used to solve the convection-diffusion equation that is divided into conservation and diffusion parts, in which the first-order accurate entropy scheme is applied to solve the conservation part and the second accurate central difference scheme is applied to solve the diffusion part. Numerical tests show that the L(infinity)error achieves about second-order accuracy, but the L-1 error reaches about forth-order accuracy.