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On a conservative upwind finite element scheme for convective diffusion equations. (English) Zbl 0466.76090


MSC:

76R99 Diffusion and convection
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:

[1] 1. K. BABA and S. YOSHII, An upwind scheme for convective diffusion equation by finite element method, Proceedings of VIIIth International Congress on Application of Mathematics in Engineering, Weimar/DDR, 1978. Zbl0386.76067 · Zbl 0386.76067
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[3] 3. P. G. CIARLET and P. A. RAVIART, General Lagrange and Hermite interpolationin Rn with applications to finite element methods, Arch. Rational Mech. AnaL,46 (1971), 177-199. Zbl0243.41004 MR336957 · Zbl 0243.41004 · doi:10.1007/BF00252458
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[6] 6. R. GORENFLO, Energy conserving discretizations of diffusion equations, Paper submitted for publication in the Proceedings of the Conference on Numerical Methods in Keszthely/Hungary, 1977. Zbl0466.76086 · Zbl 0466.76086
[7] 7. F. C. HEINRICH, P. S. HUYAKORN, O. C. ZIENKIEWICZ and A. R. MITCHELL, An ” upwind ”finite element scheme for two dimensional convective-transport equation,Int. J. Num. Meth. Engng., 11 (1977), 131-143. Zbl0353.65065 · Zbl 0353.65065 · doi:10.1002/nme.1620110113
[8] 8. F. C. HEINRICH and O. C. ZIENKIEWICZ, The finite element method and ” upwinding ” techniques in the numerical solution of confection dominated flow problems, Preprint for the ASME winter annual meeting on fini te element methods for convection dominated flows, 1979. Zbl0436.76062 · Zbl 0436.76062
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[12] 12. M. TABATA, A finite element approximation corresponding to the upwind finite differencing, Memoirs of Numerical Mathematics, 4 (1977), 47-63. Zbl0358.65102 MR448957 · Zbl 0358.65102
[13] 13. M. TABATA, Uniform convergence of the upwind finite element approximation for semilinear parabolic problems, J. Math. Kyoto Univ., 18 (1978), 327-351. Zbl0391.65038 MR495024 · Zbl 0391.65038
[14] 14. M. TABATA, L \infty -analysis of the finite element method, Lecture Notes in Num. Appl. Anal, 1 (1979) 25-62, Kinokuniya, Tokyo. Zbl0458.65096 MR690436 · Zbl 0458.65096
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