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Hughes, Thomas J. R.; Franca, Leopoldo P.; Mallet, Michel

A new finite element formulation for computational fluid dynamics. VI. Convergence analysis of the generalized SUPG formulation for linear time- dependent multidimensional advective-diffusive systems. (English) Zbl 0635.76066

Comput. Methods Appl. Mech. Eng. 63, 97-112 (1987).
[For part V see the authors, ibid. 59, 85-99 (1986; Zbl 0622.76077).]
An SUPG-type finite element method for linear symmetric multidimensional advective-diffusive systems is described and analyzed. Optimal and near optimal error estimates are obtained for the complete range of advective- diffusive behavior.

Cited in 2 Reviews
Cited in 103 Documents

MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
80A20 Heat and mass transfer, heat flow (MSC2010)
65Z05 Applications to the sciences
76R99 Diffusion and convection

Keywords:

SUPG-type finite element method; linear symmetric multidimensional advective-diffusive systems; near optimal error estimates

Citations:

Zbl 0587.76120; Zbl 0622.76075; Zbl 0622.76074; Zbl 0572.76068; Zbl 0635.76067; Zbl 0622.76077
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\textit{T. J. R. Hughes} et al., Comput. Methods Appl. Mech. Eng. 63, 97--112 (1987; Zbl 0635.76066)
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References:

[1] D. Arnold, R. Falk and R. Scott, Private communication, 1986.
[2] Hughes, T.J.R.; Franca, L.P.; Mallet, M., A new finite element method for computational fluid dynamics: I. symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics, Comput. meths. appl. mech. engrg., 54, 223-234, (1986) · Zbl 0572.76068
[3] Hughes, T.J.R.; Mallet, M., A new finite element method for computational fluid dynamics: III. the generalized streamline operator for multidimensional advection-diffusion systems, Comput. meths. appl. mech. engrg., 58, 305-328, (1986) · Zbl 0622.76075
[4] Johnson, C., Streamline methods for problems in fluid mechanics, (), 251-261
[5] Johnson, C.; Nävert, U.; Pitkäranta, J., Finite element methods for linear hyperbolic problems, Comput. meths. appl. mech. engrg., 45, 285-312, (1984) · Zbl 0526.76087
[6] Johnson, C.; Szepessy, A., On the convergence of streamline diffusion finite element methods for hyperbolic conservation laws, (), 75-91
[7] Nävert, U., A finite element method for convection-diffusion problems, ()
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.