Convergence analysis for a finite element approximation of a steady model for electrorheological fluids. (English) Zbl 1457.65180
Summary: In this paper we study the finite element approximation of systems of \({p(\cdot )}\)-Stokes type, where \({p(\cdot )}\) is a (non constant) given function of the space variables. We derive – in some cases optimal – error estimates for finite element approximation of the velocity and of the pressure, in a suitable functional setting.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 35J60 | Nonlinear elliptic equations |
| 76A05 | Non-Newtonian fluids |
| 78A30 | Electro- and magnetostatics |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 35Q35 | PDEs in connection with fluid mechanics |
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