Stabilized mixed finite element method for a quasistatic Maxwell viscoelastic model

This paper considers a stabilized mixed finite element method (MFE) for a quasistatic Maxwell viscoelastic model based on the L2(Ω)×H1(Ω) variational framework. The spatial discretization uses arbitrary degree piecewise polynomials Pl−Pk(l≥0,k≥1) to approximate stress and velocity. The temporal discretization in the fully discrete method adopts a backward Euler difference scheme. We give a unified analysis to show the stability of the semi-discrete and fully discrete solutions and derive the corresponding priori error estimates. Numerical examples are provided to support the theoretical analysis.