Analysis of the PSPG stabilization for the continuous-in-time discretization of the evolutionary stokes equations

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Date
2013
Volume
1874
Issue
Journal
Series Titel
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract

Optimal error estimates for the pressure stabilized Petrov-Galerkin (PSPG) method for the continuous-in-time discretization of the evolutionary Stokes equations are proved in the case of regular solutions. The main result is applicable to higher order finite elements. The error bounds for the pressure depend on the error of the pressure at the initial time. An approach is suggested for choosing the discrete initial velocity in such a way that this error is bounded. The "instability of the discrete pressure for small time steps", which is reported in the literature, is discussed on the basis of the analytical results. Numerical studies confirm the theoretical results, showing in particular that this instability does not occur for the proposed initial condition.

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Keywords
Parabolic Anderson model, random Schrödinger operator, eigenvalue order statistics, Poisson point process convergence, Anderson localisation
Citation
John, V., & Novo, J. (2013). Analysis of the PSPG stabilization for the continuous-in-time discretization of the evolutionary stokes equations (Vol. 1874). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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