Abstract
We consider the Streamline upwind/Petrov–Galerkin (SUPG) finite element method for two–dimensional steady scalar convection–diffusion equations and propose a new definition of the SUPG stabilization parameter along outflow Dirichlet boundaries. Numerical results demonstrate a significant improvement of the accuracy and show that, in some cases, even nodally exact solutions are obtained.
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Bazilevs, Y., Hughes, T.J.R.: Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput. & Fluids 36, 12–26 (2007)
Brooks, A.N., Hughes, T.J.R.: Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput. Methods Appl. Mech. Engrg. 32, 199–259 (1982)
Christie, I., Griffiths, D.F., Mitchell, A.R., Zienkiewicz, O.C.: Finite element methods for second order differential equations with significant first derivatives. Internat. J. Numer. Methods Engrg. 10, 1389–1396 (1976)
Ciarlet, P.G.: Basic error estimates for elliptic problems. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis, vol. 2, pp. 17–351. Finite Element Methods (pt. 1). North–Holland, Amsterdam (1991)
Grasman, J.: On the Birth of Boundary Layers. Mathematical Centre Tracts, vol. 36. Mathematical Centre, Amsterdam (1971)
John, V., Knobloch, P.: On spurious oscillations at layers diminishing (SOLD) methods for convection–diffusion equations: part I – a review. Comput. Methods Appl. Mech. Engrg. 196, 2197–2215 (2007)
Knobloch, P.: Improvements of the Mizukami–Hughes method for convection–diffusion equations. Comput. Methods Appl. Mech. Engrg. 196, 579–594 (2006)
Madden, N., Stynes, M.: Linear enhancements of the streamline diffusion method for convection–diffusion problems. Comput. Math. Appl. 32, 29–42 (1996)
Madden, N., Stynes, M.: Efficient generation of oriented meshes for solving convection–diffusion problems. Internat. J. Numer. Methods Engrg. 40, 565–576 (1997)
Roos, H.–G., Stynes, M., Tobiska, L.: Numerical Methods for Singularly Perturbed Differential Equations. Convection–Diffusion and Flow Problems, 2nd edn. Springer, Berlin (2008)
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Communicated by Martin Stynes.
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Knobloch, P. On the choice of the SUPG parameter at outflow boundary layers. Adv Comput Math 31, 369 (2009). https://doi.org/10.1007/s10444-008-9075-6
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DOI: https://doi.org/10.1007/s10444-008-9075-6
Keywords
- Convection–diffusion equations
- Streamline upwind/Petrov–Galerkin (SUPG) method
- Spurious oscillations
- Outflow boundary layers
- Singularly perturbed problems