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


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


[1] Adam, Y., Finite difference methods for convective-diffusive equations, ()
[2] Zienkiewicz, O.C.; Gallagher, R.H.; Hood, P., Newtonian and non-Newtonian viscous incompressible flow. temperature induced flows. finite element solution, ()
[3] Piva, R.; diCarlo, A., Numerical techniques for convection diffusion problems, ()
[4] Miller, J.S.H., A finite element method for a two point boundary value problem with a small parameter affecting the highest derivative, (), School of Mathematics · Zbl 0384.65040
[5] Blackburn, W.S., Letter to the editor, Internat. J. numer. meths. engrg., 10, 718-719, (1976)
[6] Christies, I.; Griffiths, D.F.; Mitchell, A.R.; Zienkiewicz, O.C., Finite element methods for second order differential equations with significant first derivatives, Internat. J. numer. meths. engrg., 10, 1389-1396, (1976) · Zbl 0342.65065
[7] Heinrich, J.C.; Huyakorn, P.S.; Zienkiewicz, O.C.; Mitchell, A.R., An ‘upwind’ finite element scheme for two-dimensional convective-transport equation, Internat. J. numer. meths. engrg., 11, 131-143, (1977) · Zbl 0353.65065
[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
[9] Tabata, M., A finite element approximation corresponding to the upwind finite differencing, Mem. numer. math., 4, 47-63, (1977) · Zbl 0358.65102
[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, (), to appear. · Zbl 0514.76083
[13] Nguyen, H.; Reynen, J., A space-time finite element method for hyperbolic equations, () · Zbl 0517.76089
[14] Reynen, J.; Nguyen, H., CFEM—A finite element based analysis of two-phase channel flow, () · 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, () · Zbl 0574.76053
[17] Raithby, G.D., Skew upstream differencing schemes for problems involving fluid flow, Comput. meths. appl. mech. engrg., 9, 153-164, (1976) · Zbl 0347.76066
[18] Griffiths, D.F.; Mitchell, A.R., On generating upwind finite element methods, () · Zbl 0423.76069
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.