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.

本文的目的是建立带有标量辅助变量的粘弹性Kelvin-Voigt模型的Euler隐式/显式方案的无条件稳定性结果。我们首先将Kelvin-Voigt模型重新构造为具有三个变量的等效系统。标准的Galerkin有限元方法用于近似空间离散化。然后采用欧拉隐式/显式方法离散考虑的问题，形成一个常数系数代数系统，可以有效地求解该问题。建立了各种规范中数值解的无条件耗能和稳定性结果。最佳误差估计也由能量方法和Gronwall引理给出。最后，