Stabilization Strategies for High Order Methods for Transport Dominated Problems

作者: Alfio Quarteroni , Erik Burman , Benjamin Stamm

DOI:

关键词: Stability (probability)High orderSpectral methodApplied mathematicsMathematicsMathematical optimizationFinite element methodGalerkin method

摘要: Standard high order Galerkin methods, such as pure spectral or finite element have insufficient stability properties when applied to transport dominated problems. In this paper we review some stabilization strategies for methods and multidomain approaches.

参考文章(37)
Roland Becker, Malte Braack, A Two-Level Stabilization Scheme for the Navier-Stokes Equations Numerical Mathematics and Advanced Applications. pp. 123- 130 ,(2004) , 10.1007/978-3-642-18775-9_9
Hans-Görg Roos, Martin Stynes, Lutz Tobiska, Numerical Methods for Singularly Perturbed Differential Equations Springer Series in Computational Mathematics. ,(1996) , 10.1007/978-3-662-03206-0
P. LASAINT, P.A. RAVIART, On a Finite Element Method for Solving the Neutron Transport Equation Mathematical Aspects of Finite Elements in Partial Differential Equations#R##N#Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, April 1–3, 1974. pp. 1- 40 ,(1974) , 10.1016/B978-0-12-208350-1.50008-X
Jim Douglas, Todd Dupont, Interior Penalty Procedures for Elliptic and Parabolic Galerkin Methods Computing Methods in Applied Sciences. ,vol. 58, pp. 207- 216 ,(1976) , 10.1007/BFB0120591
Eitan Tadmor, Convergence of spectral methods for nonlinear conservation laws SIAM Journal on Numerical Analysis. ,vol. 26, pp. 30- 44 ,(1989) , 10.1137/0726003
Herv� Vandeven, Family of spectral filters for discontinuous problems Journal of Scientific Computing. ,vol. 6, pp. 159- 192 ,(1991) , 10.1007/BF01062118
FRANCO BREZZI, ALESSANDRO RUSSO, CHOOSING BUBBLES FOR ADVECTION-DIFFUSION PROBLEMS Mathematical Models and Methods in Applied Sciences. ,vol. 04, pp. 571- 587 ,(1994) , 10.1142/S0218202594000327
G. Rosatti, L. Bonaventura, A. Deponti, G. Garegnani, An Accurate and Efficient Semi-Implicit Method for Section Averaged Free Surface Flow Modelling International Journal for Numerical Methods in Fluids. ,vol. 65, pp. 448- 473 ,(2011) , 10.1002/FLD.2191