An adaptive virtual element method for incompressible flow. (1st November 2021) - Wang, Ying; Wang, Gang; Wang, Feng
Abstract: In this paper, we firstly present and analyze a residual-type a posteriori error estimator for a low-order virtual element discretization for the Stokes problem on general polygonal meshes. We prove that this estimator yields globally upper and locally lower bounds for the discretization error. Then, we extend the estimator to the Navier-Stokes problem. In order to deal with the case of small viscosity, we modify the discrete bilinear form following the idea of variational multiscale method. Since the virtual element method naturally handles hanging nodes, the mesh refinement can exploit them without any local refinement to recover mesh conformity. A series of benchmark tests are reported to verify the effectiveness and flexibility of the designed error estimator when it is combined with adaptive mesh refinement.