Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows

Abstract

We carry out in this paper a rigorous error analysis for a finite element discretization of the scalar auxiliary variable (SAV) schemes. The finite-element method we study is a Galerkin method with standard Lagrange elements based on a mixed variational formulation. We derive optimal error estimates for both the first- and second-order SAV schemes with the finite-element method in space.