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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

[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.

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
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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
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[7] Nävert, U., A finite element method for convection-diffusion problems, ()
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