Stabilized finite volume element method for the 2D nonlinear incompressible viscoelastic flow equation

Abstract In this article, we devote ourselves to building a stabilized finite volume element (SFVE) method with a non-dimensional real together with two Gaussian quadratures of the nonlinear incompressible viscoelastic flow equation in a two-dimensional (2D) domain, analyzing the existence, stability, and error estimates of the SFVE solutions and verifying the validity of the preceding theoretical conclusions by numerical simulations.