Adaptive finite volume methods for steady convection-diffusion equations with mesh optimization

Abstract

An adaptive algorithm for steady convection-diffusion problems that combines a posteriori error estimation with conforming centroidal Voronoi Delaunay triangulations (CfCVDTs) is proposed and tested in two dimensional domains. Different from most current adaptive methods, this algorithm realizes mesh refinement and coarsening implicitly at each level by nodes insertion and redistribution. Especially, the nodes redistribution is implemented through the generation of CfCVDTs with some density function derived from the a posteriori error estimators for the problem. Numerical experiments show that the convergence rates achieved are almost the best obtainable using the linear finite volume discretizations and the resulting meshes always maintain high quality.