Semi-implicit Euler Scheme for Generalized Newtonian Fluids

Rheological behavior of certain non–Newtonian fluids in engineering sciences is often modeled by power law ansatzes with p ≤ 2. So far, existing numerical analysis for local strong solutions study a fully implicit time discretization and find only restricted ranges of admissible p’s for corresponding error estimates [9]; different nonlinear stabilization strategies which allow a corresponding error analysis for smaller p’s are examined in [2, 3]. In the present paper, a semi implicit time discretization scheme is proposed, and error estimates apply to the extended range p ∈ ( 3 2 , 2]. The key analytical tool is a new Gronwall–type inequality.