The Euler implicit/explicit FEM for the Kelvin–Voigt model based on the scalar auxiliary variable (SAV) approach

Abstract

The objective of this paper is to establish the unconditional stability results of Euler implicit/explicit scheme for the viscoelastic Kelvin–Voigt model with a scalar auxiliary variable. We first reformulate the Kelvin–Voigt model into an equivalent system with three variables. The standard Galerkin finite element method is used to approximate the spatial discretization. Then the Euler implicit/explicit method is adopted to discrete the considered problem, a constant coefficient algebraic system is formed and it can be solved efficiently. The unconditional energy dissipation and stability results of numerical solutions in various norms are established. Optimal error estimates are also presented by the energy method and the Gronwall lemma. Finally, some numerical results are given to verify the established theoretical findings and show the performances of the considered numerical scheme.