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A space-time least-square finite element scheme for advection-diffusion equations. (English) Zbl 0517.76089


MSC:

76R99 Diffusion and convection
76M99 Basic methods in fluid mechanics
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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References:

[1] Adam, Y., Finite difference methods for convective-diffusive equations, (Introduction to Computational Fluid Dynamics. Introduction to Computational Fluid Dynamics, Lecture Series 1983-01 (1983), VKI)
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[8] Heinrich, J. C.; Zienkiewicz, O. C., Quadratic finite element schemes for two-dimensional convective transport problems, Internat. J. Numer. Meths. Engrg., 11, 1831-1844 (1977) · Zbl 0372.76002
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[10] Tabata, M., Uniform convergence of the upwind finite element approximation for semilinear parabolic problems, J. Math. Kyoto Univ., 18, 327-351 (1978) · Zbl 0391.65038
[11] Hughes, T. J.R., A simple scheme for developing ‘upwind’ finite elements, Internat. J. Numer. Meths. Engrg., 12, 1359-1365 (1978) · Zbl 0393.65044
[12] Donea, J.; Giuliani, S.; Laval, H.; Quartapelle, L., Time accurate solution of advection-diffusion problems by finite elements, (Hughes, T. J.R., Comput. Meths. Appl. Mech. Engrg. (1984)), to appear. · Zbl 0514.76083
[13] Nguyen, H.; Reynen, J., A space-time finite element method for hyperbolic equations, (Proc. 3rd Internat. Symp. on Numerical Methods in Engineering. Proc. 3rd Internat. Symp. on Numerical Methods in Engineering, Paris (1983)) · Zbl 0517.76089
[14] Reynen, J.; Nguyen, H., CFEM—A finite element based analysis of two-phase channel flow, (Proc. LMFBR Safety Topical Meeting. Proc. LMFBR Safety Topical Meeting, Lyon-Ecully (1982)) · Zbl 0506.76106
[15] Christie, I.; Mitchell, A. R., Upwinding of high order Galerkin methods in conduction-convection problems, Internat. J. Numer. Meths. Engrg., 12, 1764-1771 (1978) · Zbl 0391.65034
[16] Nguyen, H.; Reynen, J., A space-time finite element approach to Burgers’ equation, (Presentation at 2nd Internat. Conf. Numerical Methods for Nonlinear Problems. Presentation at 2nd Internat. Conf. Numerical Methods for Nonlinear Problems, Barcelon (April 1984)) · Zbl 0574.76053
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