Staggered Discontinuous Galerkin Method for Singular Power-law Systems

In this paper, we study singular power-law models of shear thinning, which is characterized by unbounded viscosity at the zero shear-rate limit, and we study the staggered discontinuous Galerkin method for p-Stokes type systems for p ∈ (1,2]. We use Picard’s iterate method to solve the correspondent nonlinear system. If p is very close to 1, when solving discrete nonlinear equations using the Picard method, numerical instabilities often occur. We give the numerical stability method of singular power-law system and some numerical experiments by reference [1].