@article{M2AN_1988__22_3_477_0, author = {Lube, G.}, title = {Uniform in $\varepsilon $ discretization error estimates for convection dominated convection-diffusion problems}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {477--498}, publisher = {AFCET - Gauthier-Villars}, address = {Paris}, volume = {22}, number = {3}, year = {1988}, mrnumber = {958880}, zbl = {0659.65092}, language = {en}, url = {http://archive.numdam.org/item/M2AN_1988__22_3_477_0/} }
TY - JOUR AU - Lube, G. TI - Uniform in $\varepsilon $ discretization error estimates for convection dominated convection-diffusion problems JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1988 SP - 477 EP - 498 VL - 22 IS - 3 PB - AFCET - Gauthier-Villars PP - Paris UR - http://archive.numdam.org/item/M2AN_1988__22_3_477_0/ LA - en ID - M2AN_1988__22_3_477_0 ER -
%0 Journal Article %A Lube, G. %T Uniform in $\varepsilon $ discretization error estimates for convection dominated convection-diffusion problems %J ESAIM: Modélisation mathématique et analyse numérique %D 1988 %P 477-498 %V 22 %N 3 %I AFCET - Gauthier-Villars %C Paris %U http://archive.numdam.org/item/M2AN_1988__22_3_477_0/ %G en %F M2AN_1988__22_3_477_0
Lube, G. Uniform in $\varepsilon $ discretization error estimates for convection dominated convection-diffusion problems. ESAIM: Modélisation mathématique et analyse numérique, Tome 22 (1988) no. 3, pp. 477-498. http://archive.numdam.org/item/M2AN_1988__22_3_477_0/
[1] Stability and error estimates of Galerkin finite element approximations for convection-diffusion equations, I.M.A. Journal Num. Anal., 1 (1981), 329-345 | MR | Zbl
,[2] On the numerical solution of convection dominated convection-diffusion problems, in : Proc. Tagung Math. Physik, Karl-Marx-Stadt 1983,Teubner-Texte, Leipzig 1984. | MR | Zbl
,[3] Maximal positive boundary value problems as limits of singular perturbations problems, Transact. Amer. Math. Soc, 270 (1982) 2,377-400. | MR | Zbl
, ,[4] The asymptotic behaviour of the first real eigenvalue of second order elliptic operators with a small parameter in the highest derivatives II. Indiana Univ. Math. J., 23 (1974), 991-1011. | MR | Zbl
, , ,[5] Application of a generalized maximum principle to estimate the corner layers in the n-dimensional case, in : Singularly perturbed differential equations and applications (J. Förste ed.), Akademie der Wissenschaften der DDR, Inst. f. Math., Report R-Mech 03/84, Berlin 1984, 1-8.
,[6] A numerical study of the steady scalar convective diffusion equation for small viscosity, J. Comput. Phys. 56 (1984), 513-529. | MR | Zbl
, ,[7] Singularly perturbed differential equations, Math. Research, v. 13, Akademie-Verlag Berlin 1983. | MR | Zbl
, , , , ,[8] multidimensional upwind scheme with no crosswind diffusion, in : AMD v. 34, Finite element methods for convection dominated flows (T. J. R. Hughes ed.), ASME, New York, 1979. | MR | Zbl
, ,[9] On a difference scheme for the équation , in : Difference methods for solving boundary value problems containing a small parameter and discontinuous boundary conditions, Isd. Uralskovo nacn. centra AN SSSR, Swerdlowsk 1976, 19-37 (russ.).
,[10] Finite element methods for linear hyperbolic problems, Comp. Meth. Appl. Mech. Engrg. 45 (1984), 285-312. | MR | Zbl
, , ,[11] Analysis of a difference approximation for a singular perturbation problem in two dimensions, in : Proc. Conf. Boundary and interior layers - computational and asymptotic methods (J. J. H. Miller ed.), Dublin 1980, Boole Press 1980, 113-117. | MR | Zbl
,[12] On the convergence, uniformly in , of difference schemes for a two point boundary value problem, in : Numerical analysis of singular perturbation problems (P. W. Hemker and J. J. H. Miller, eds.), Academic Press, London, New York, San Francisco 1979, 467-474. | MR | Zbl
,[13]A Petrov-Galerkin finite element method for solving convection dominated flows : an accurate upwinding technique for satisfying the maximum principle, Comp. Meth. Appl. Mech. Engrg. 50 (1985),181-193. | MR | Zbl
, ,[14] A finite element method for convection-diffusion problems, Thesis, Chalmers Univ. of Technol., Gothenburg, Sweden 1982.
,[15] On a three-point difference scheme for a singular perturbation problem without a first derivative term, Mem. Num. Math. 7 (1980). | MR | Zbl
,[16] Maximum principles in differential equations, Englewood Cliffs, New Jersey, Prentice-Hall, Inc., 1967. | MR | Zbl
, ,Ein hybrides upwind-FEM-Verfahren und dessen Anwendung auf schwach gekoppelte elliptische Differentialgleichungen mit dominanter Konvektion, Dissertation, Techn. Hochschule Magdeburg 1986.
,[18] On the finite element method for singularly perturbed reaction-diffusion problems in two and one dimension, Math. Comp.40 (1983), 47-89. | MR | Zbl
, ,[19] Eine asymptotisch angepafite Finite-Element-Methode fur singulär gestörte elliptische Randwertaufgaben, Dissertation, Techn. Hochschule Magdeburg 1986.
,[20] Solution of a boundary value problem for an elliptic equation with a small parameter affecting the highest derivatives, Shurnal Vytsch. Mat. Mat. Fis., 26 (1986), 1019-1031 (russ.). | MR | Zbl
,[21] A différence scheme for a differential equation with two small parameters affecting the derivatives, Numer. Meth. Mechs. Cont. Media, 7 (1976), 145-155. (russ.) | MR
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