Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Error estimators for nonconforming finite element approximations of the Stokes problem
Mathematics of Computation
A Posteriori Error Estimators for Nonconforming Approximation of Some Quasi-Newtonian Flows
SIAM Journal on Numerical Analysis
New Finite Element Methods in Computational Fluid Dynamics by H(div) Elements
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
Augmented Mixed Finite Element Methods for the Stationary Stokes Equations
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Mixed Finite Element Methods for Incompressible Flow: Stationary Navier-Stokes Equations
SIAM Journal on Numerical Analysis
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This paper establishes a posteriori error analysis for the Stokes equations discretized by an interior penalty type method using $H(\mathrm{div})$ finite elements. The a posteriori error estimator is then employed for designing two grid refinement strategies; one is locally based and the other is globally based. The locally based refinement technique is believed to be able to capture local singularities in the numerical solution. The numerical formulations for the Stokes problem make use of $H(\mathrm{div})$ conforming elements of Raviart-Thomas type. Therefore, the finite element solution features a full satisfaction of the continuity equation (mass conservation). The result of this paper provides a rigorous analysis for the method's reliability and efficiency. In particular, an $H^1$ norm a posteriori error estimator is obtained, together with upper and lower bound estimates. Numerical results are presented to verify the new theory of a posteriori error estimators.