Analysis of accuracy of a finite volume scheme for diffusion equations on distorted meshes

We investigate the convergence of a finite volume scheme for the approximation of diffusion operators on distorted meshes. The method was originally introduced by Hermeline [F. Hermeline, A finite volume method for the approximation of diffusion operators on distorted meshes, J. Comput. Phys. 160 (2000) 481–499], which has the advantage that highly distorted meshes can be used without the numerical results being altered. In this work, we prove that this method is of first-order accuracy on highly distorted meshes. The results are further extended to the diffusion problems with discontinuous coefficient and non-stationary diffusion problems. Numerical experiments are carried out to confirm the theoretical predications.