NDLI: Analysis of the Pressure Stabilized Petrov--Galerkin Method for the Evolutionary Stokes Equations Avoiding Time Step Restrictions

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Novo, Julia John, Volker
Copyright Year	2015
Abstract	Optimal error estimates for the pressure stabilized Petrov--Galerkin method for the evolutionary Stokes equations are proved, in the case of regular solutions, without restriction on the length of the time step. These results clarify the instability of the discrete pressure for small time steps reported in the literature. First, the limit situation of the continuous-in-time discretization is considered and second the numerical analysis for the backward Euler scheme is carried out. The main results are applicable to higher order finite elements. The analytical results are strongly based on an appropriate approach for computing the initial velocity, which is suggested in this paper. Numerical studies confirm the theoretical results, showing in particular that this instability does not occur for the proposed initial condition.
Starting Page	1005
Ending Page	1031
Page Count	27
File Format	PDF
ISSN	00361429
DOI	10.1137/130944941
e-ISSN	10957170
Issue Number	2
Volume Number	53
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2015-04-09
Access Restriction	Subscribed
Subject Keyword	Stability and convergence of numerical methods PSPG stabilization equal order pairs of finite element spaces backward Euler scheme small time step instability optimal error estimates Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods evolutionary Stokes equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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