Computer Methods in Applied Mechanics and Engineering
A posteriori error estimates for the Stokes problem
SIAM Journal on Numerical Analysis
Error analysis of some Galerkin least squares methods for the elasticity equations
SIAM Journal on Numerical Analysis
Stabilized finite element methods. II: The incompressible Navier-Stokes equations
Computer Methods in Applied Mechanics and Engineering
Mathematics of Computation
Anisotropic mesh refinement for a singularly perturbed reaction diffusion model problem
Applied Numerical Mathematics
Superconvergence of Finite Element Approximations for the Stokes Problem by Projection Methods
SIAM Journal on Numerical Analysis
The Stability of Mixed hp-Finite Element Methods for Stokes Flow on High Aspect Ratio Elements
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Stability of discretizations of the Stokes problem on anisotropic meshes
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
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An adaptive algorithm is proposed for solving the Stokes problem with continuous, piecewise linear stabilized finite elements and meshes with high aspect ratio. Anisotropic, a posteriori error estimates in the H^1xL^2 norm are derived, the constant being independent from the mesh aspect ratio. The estimates involve the first derivatives of the velocity error and the velocity of a dual problem having the pressure error in the right side. An explicit error indicator is then proposed. The first derivatives of the velocity error are approximated using Zienkiewicz-Zhu error estimator (post-processing). The pressure error in the right side of the dual problem is approximated by smoothing. Numerical results on meshes with large aspect ratio show that the error indicator is robust whenever the pressure error in the dual problem is approximated with sufficient accuracy. Finally, an adaptive algorithm is proposed, with goal to build an anisotropic triangulation such that the relative estimated error is close to a preset tolerance.