A new finite element formulation for computational fluid dynamics. III: The generalized streamline operator for multidimensional advective- diffusive systems. (English) Zbl 0622.76075

Hughes, Thomas J. R.; Mallet, Michel

Comput. Methods Appl. Mech. Eng. 58, 305-328 (1986).

[For part II see the summary above (Zbl 0622.76074).]
A finite element method based on the SUPG concept is presented for multidimensional advective-diffusive systems. Error estimates for the linear case are established which are valid over the full range of advective-diffusive phenomena.

MSC:

76N10	Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
80A20	Heat and mass transfer, heat flow (MSC2010)
76N15	Gas dynamics (general theory)
76R99	Diffusion and convection
65Z05	Applications to the sciences

Keywords:

streamline-upwind/Petrov-Galerkin concept; one-dimensional systems; finite element method; diffusive systems; advective-diffusive phenomena

Citations:

Zbl 0572.76068; Zbl 0581.76077; Zbl 0587.76120; Zbl 0622.76076; Zbl 0622.76077; Zbl 0622.76074

References:

[1]	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. Meths. Appl. Mech. Engrg., 32, 199-259 (1982) · Zbl 0497.76041
[2]	Donéa, J., A Taylor-Galerkin method for convective transport problems, Internat. J. Numer. Meths. Engrg., 20, 1, 101-119 (1984) · Zbl 0524.65071
[3]	Dutt, P. K., Stable boundary conditions and difference schemes for Navier-Stokes type equations, (Ph.D. Thesis (1985), University of California: University of California Los Angeles, CA) · Zbl 0701.76032
[4]	Harten, A., On the symmetric form of systems of conservation laws with entropy, J. Comput. Phys., 49, 151-164 (1983) · Zbl 0503.76088
[5]	Hoger, A.; Carlson, D. E., Determination of the stretch and rotation in the polar decomposition of the deformation gradient, Quart. Appl. Math., 42, 1, 113-117 (1984) · Zbl 0551.73004
[6]	Hughes, T. J.R.; Franca, L. P.; Mallet, M., A new finite element formulation 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
[7]	Hughes, T. J.R.; Mallet, M.; Mizukami, A., A new finite element formulation for computational fluid dynamics: II. Beyond SUPG, Comput. Meths. Appl. Mech. Engrg., 54, 341-355 (1986) · Zbl 0622.76074
[8]	Hughes, T. J.R.; Tezduyar, T. E., Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations, Comput. Meths. Appl. Mech. Engrg., 45, 217-284 (1984) · Zbl 0542.76093
[9]	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
[10]	Marsden, J. E.; Hughes, T. J.R., Mathematical Foundations of Elasticity (1983), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0545.73031
[11]	Tadmor, E., Skew-selfadjoint forms for systems of conservation laws, J. Math. Anal. Appl., 103, 428-442 (1984) · Zbl 0599.35102