A posteriori error estimates for the Stokes problem
SIAM Journal on Numerical Analysis
A Posteriori Error Estimators for the Stokes and Oseen Equations
SIAM Journal on Numerical Analysis
A Posteriori Error Estimation for Stabilized Mixed Approximations of the Stokes Equations
SIAM Journal on Scientific Computing
Algorithm 866: IFISS, a Matlab toolbox for modelling incompressible flow
ACM Transactions on Mathematical Software (TOMS)
An Optimal Iterative Solver for Symmetric Indefinite Systems Stemming from Mixed Approximation
ACM Transactions on Mathematical Software (TOMS)
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The implementation of quadratic velocity, linear pressure finite element approximation methods for the steady-state incompressible (Navier-)Stokes equations is addressed in this work. Three types of a posteriori error indicator are introduced and are shown to give global error estimates that are equivalent to the true discretisation error. Computational results suggest that the solution of local Poisson problems provides a cost-effective error estimation strategy, both from the perspective of accurate estimation of the global error and for the purpose of selecting elements for refinement within a contemporary self-adaptive refinement algorithm.