Stability of Streamline Upwind Petrov-Galerkin (SUPG) finite elements for transient advection-diffusion problems.

Journal Article · Mon Sep 01 04:00:00 EDT 2003 · Proposed for publication in Journal of Computer Methods in Application and Mechanical Engineering.

OSTI ID:1005399

Shadid, John Nicolas; Bochev, Pavel Blagoveston; Gunzburger, Max Donald ^[1]

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1. Florida State University, Tallahasse, FL

Implicit time integration coupled with SUPG discretization in space leads to additional terms that provide consistency and improve the phase accuracy for convection dominated flows. Recently, it has been suggested that for small Courant numbers these terms may dominate the streamline diffusion term, ostensibly causing destabilization of the SUPG method. While consistent with a straightforward finite element stability analysis, this contention is not supported by computational experiments and contradicts earlier Von-Neumann stability analyses of the semidiscrete SUPG equations. This prompts us to re-examine finite element stability of the fully discrete SUPG equations. A careful analysis of the additional terms reveals that, regardless of the time step size, they are always dominated by the consistent mass matrix. Consequently, SUPG cannot be destabilized for small Courant numbers. Numerical results that illustrate our conclusions are reported.

• Research Organization: Sandia National Laboratories
• Sponsoring Organization: USDOE
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 1005399
• Report Number(s): SAND2003-3576J
• Journal Information: Proposed for publication in Journal of Computer Methods in Application and Mechanical Engineering., Journal Name: Proposed for publication in Journal of Computer Methods in Application and Mechanical Engineering. Journal Issue: 23-26 Vol. 193; ISSN 0045-7825; ISSN CMMECC
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ACCURACY
CONVECTION
DIFFUSION
FINITE ELEMENT METHOD
GALERKIN-PETROV METHOD
STABILITY
TRANSIENTS