Analysis of HDG Methods for Oseen Equations

Analysis of HDG Methods for Oseen Equations

We propose a hybridizable discontinuous Galerkin (HDG) method to numerically solve the Oseen equations which can be seen as the linearized version of the incompressible Navier-Stokes equations. We use same polynomial degree to approximate the velocity, its gradient and the pressure. With a special p...

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Veröffentlicht in:Journal of scientific computing 2013-05, Vol.55 (2), p.392-431
Hauptverfasser: Cesmelioglu, Aycil, Cockburn, Bernardo, Nguyen, Ngoc Cuong, Peraire, Jaume
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Convergence
Eigenvalues
Eigenvectors
Error analysis
Galerkin methods
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Navier-Stokes equations
Optimization
Polynomials
Projection
Reynolds number
Theoretical
Velocity
Velocity gradient
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Zusammenfassung:We propose a hybridizable discontinuous Galerkin (HDG) method to numerically solve the Oseen equations which can be seen as the linearized version of the incompressible Navier-Stokes equations. We use same polynomial degree to approximate the velocity, its gradient and the pressure. With a special projection and postprocessing, we obtain optimal convergence for the velocity gradient and pressure and superconvergence for the velocity. Numerical results supporting our theoretical results are provided.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-012-9639-y