Hopf bifurcation of reaction-diffusion and Navier-Stokes equations under discretization
β Scribed by Christian Lubich; Alexander Ostermann
- Publisher
- Springer-Verlag
- Year
- 1998
- Tongue
- English
- Weight
- 224 KB
- Volume
- 81
- Category
- Article
- ISSN
- 0029-599X
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## Abstract A discretization method is presented for the full, steady, compressible NavierβStokes equations. The method makes use of quadrilateral finite volumes and consists of an upwind discretization of the convective part and a central discretization of the diffusive part. In the present paper
We derive error bounds for Runge-Kutta time discretizations of semilinear parabolic equations with nonsmooth initial data. The framework includes reaction-diffusion equations and the incompressible Navier-Stokes equations. Nonsmooth-data error bounds of the type given here are needed in the study of
The introduction into the continuity equation of additional terms to recover grid-scale ellipticity, for the Navier-Stokes equations discretised on a non-staggered mesh, results in an increase in the discretisation error. The introduced error is a combination of the additional truncation error and a