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
Algorithm 866: IFISS, a Matlab toolbox for modelling incompressible flow
ACM Transactions on Mathematical Software (TOMS)
The finite volume method based on stabilized finite element for the stationary Navier-Stokes problem
Journal of Computational and Applied Mathematics
An adaptive stabilized finite element method for the generalized Stokes problem
Journal of Computational and Applied Mathematics
An Optimal Iterative Solver for Symmetric Indefinite Systems Stemming from Mixed Approximation
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Scientific Computing
A simple yet effective a posteriori estimator for classical mixed approximation of Stokes equations
Applied Numerical Mathematics
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The practical implementation of the lowest-order Pl - P0 (linear velocity, constant pressure) finite element method for the steady-state incompressible (Navier--)Stokes equations is addressed in this work. Three different types of a posteriori error indicator are introduced and each is shown to be equivalent to the discretization error. Our numerical results show that these indicators can be used to drive an adaptive refinement process which is specially tailored to create grids which conform to the requirements of the local stabilization. It is also shown that the indicators provide an effective method for detecting local singularities in the flow solution.