Search results for "Uzawa algorithm"

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On a posteriori error bounds for approximations of the generalized Stokes problem generated by the Uzawa algorithm

2012

In this paper, we derive computable a posteriori error bounds for approximations computed by the Uzawa algorithm for the generalized Stokes problem. We show that for each Uzawa iteration both the velocity error and the pressure error are bounded from above by a constant multiplied by the L2-norm of the divergence of the velocity. The derivation of the estimates essentially uses a posteriori estimates of the functional type for the Stokes problem. peerReviewed

a posteriori error estimatesNumerical AnalysisUzawa-algoritmiApproximations of πa posteriori virhe-estimaatitUzawa algorithmgeneralized Stokes problemModeling and SimulationCalculusStokes problemA priori and a posterioriApplied mathematicsyleistetty Stokesin yhtälöMathematics
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A posteriori error estimates for variational problems in the theory of viscous fluids

2016

The papers included in the thesis are focused on functional type a posteriori error estimates for the Stokes problem, the Stokes problem with friction type boundary conditions, the Oseen problem, and the anti-plane Bingham problem. In the summary of the thesis we consider only the Oseen problem. The papers present and justify special forms of these estimates which are suitable for the approximations generated by the Uzawa algorithm. The estimates are of two main types. Estimates of the first type use exact solutions obtained on the steps of the Uzawa algorithm. They show how errors encompassed in Uzawa approximations behave and have mainly theoretical meaning. Estimates of the second type o…

osittaisdifferentiaaliyhtälötvirtauslaskentaOseen problemUzawa algorithmStokes problemnonlinear boundary conditionsalgoritmitfluiditfunctional a posteriori error estimatesBingham problemvirtausapproksimointivirheanalyysiestimointi
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