### A Posteriori Error Estimators for the Stokes Equations.

R. Vefürth (1987)

Numerische Mathematik

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R. Vefürth (1987)

Numerische Mathematik

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T.A. Porsching (1977/1978)

Numerische Mathematik

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Jie Shen (1992)

Numerische Mathematik

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Etienne Emmrich (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The incompressible Navier-Stokes problem is discretized in time by the two-step backward differentiation formula. Error estimates are proved under feasible assumptions on the regularity of the exact solution avoiding hardly fulfillable compatibility conditions. Whereas the time-weighted velocity error is of optimal second order, the time-weighted error in the pressure is of first order. Suboptimal estimates are shown for a linearisation. The results cover both the two- and three-dimensional...

Burda, Pavel, Novotný, Jaroslav, Sousedík, Bedřich, Šístek, Jakub

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We consider the Navier-Stokes equations for the incompressible flow in channels with forward and backward steps. The paper consists of two main parts. In the first part we investigate a posteriori error estimates for the Stokes and Navier-Stokes equations on two-dimensional polygonal domains. We apply the a posteriori estimates to solve an incompressible flow problem in a domain with corners that cause singularities in the solution. Second part of the paper stands on the result on the...

V. Girault, P.A. Raviart (1979)

Numerische Mathematik

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Burda, Pavel, Hasal, Martin

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We derive a residual based a posteriori error estimate for the Stokes-Brinkman problem on a two-dimensional polygonal domain. We use Taylor-Hood triangular elements. The link to the possible information on the regularity of the problem is discussed.