A divergence-free weak Galerkin method for quasi-Newtonian Stokes flows
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摘要:
This paper proposes a weak Galerkin finite element method to solve incompressible quasi-Newtonian Stokes equations.We use piecewise polynomials of degrees k + 1 (k≥ 0) and k for the velocity and pressure in the interior of elements,respectively,and piecewise polynomials of degrees k and k + 1 for the boundary parts of the velocity and pressure,respectively.Wellposedness of the discrete scheme is established.The method yields a globally divergence-free velocity approximation.Optimal priori error estimates are derived for the velocity gradient and pressure approximations.Numerical results are provided to confirm the theoretical results.