Free Access
Issue
ESAIM: M2AN
Volume 22, Number 3, 1988
Page(s) 477 - 498
DOI https://doi.org/10.1051/m2an/1988220304771
Published online 31 January 2017
  1. O. AXELSSON, Stability and error estimates of Galerkin finite element approximations for convection-diffusion equations, I.M.A. Journal Num. Anal., 1 (1981), 329-345 [MR: 641313] [Zbl: 0508.76069]
  2. O. AXELSSON, On the numerical solution of convection dominated convection-diffusion problems, in : Proc. Tagung Math. Physik, Karl-Marx-Stadt 1983,Teubner-Texte, Leipzig 1984. [MR: 781752] [Zbl: 0563.76084]
  3. C. BARDOS, J. RAUCH, Maximal positive boundary value problems as limits of singular perturbations problems, Transact. Amer. Math. Soc, 270 (1982) 2,377-400. [MR: 645322] [Zbl: 0485.35010]
  4. A. DEVINATZ, R. ELLIS, A. FRIEDMAN , 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: 344709] [Zbl: 0263.35026]
  5. A. FELGENHAUER, 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. M. B. GILLES, M. E. ROSE, A numerical study of the steady scalar convective diffusion equation for small viscosity, J. Comput. Phys. 56 (1984), 513-529. [MR: 768674] [Zbl: 0572.76087]
  7. H. GOERING, A. FELGENHAUER, G. LUBE, H. G. ROOS, L. TOBISKA, Singularly perturbed differential equations, Math. Research, v. 13, Akademie-Verlag Berlin 1983. [MR: 718115] [Zbl: 0522.35003]
  8. T. J. R. HUGHES, A. BROOKS, 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: 571679] [Zbl: 0423.76067]
  9. K. W. JEMELJANOV, On a difference scheme for the équation $\varepsilon \Delta u + au_{x_1}=f$ , 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. C. JOHNSON, U. NÄVERT, J. PITKARANTA, Finite element methods for linear hyperbolic problems, Comp. Meth. Appl. Mech. Engrg. 45 (1984), 285-312. [MR: 759811] [Zbl: 0526.76087]
  11. R. B. KELLOGG, 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: 589355] [Zbl: 0439.65081]
  12. J. J. H. MILLER, On the convergence, uniformly in $\varepsilon $, 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: 556537] [Zbl: 0419.65051]
  13. [13]A. MIZUKAMI, T. J. R. HUGHES, 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: 802339] [Zbl: 0553.76075]
  14. U. NÄVERT, A finite element method for convection-diffusion problems, Thesis, Chalmers Univ. of Technol., Gothenburg, Sweden 1982.
  15. K. NIIJIMA, On a three-point difference scheme for a singular perturbation problem without a first derivative term, Mem. Num. Math. 7 (1980). [MR: 588462] [Zbl: 0484.65054]
  16. M. H. PROTTER, H. F. WEINBERGER, Maximum principles in differential equations, Englewood Cliffs, New Jersey, Prentice-Hall, Inc., 1967. [MR: 219861] [Zbl: 0153.13602]
  17. [17] U. RISCH, Ein hybrides upwind-FEM-Verfahren und dessen Anwendung auf schwach gekoppelte elliptische Differentialgleichungen mit dominanter Konvektion, Dissertation, Techn. Hochschule Magdeburg 1986.
  18. A. M. SCHATZ, L. B. WAHLBIN, On the finite element method for singularly perturbed reaction-diffusion problems in two and one dimension, Math. Comp.40 (1983), 47-89. [MR: 679434] [Zbl: 0518.65080]
  19. F. SCHIEWECK, Eine asymptotisch angepafite Finite-Element-Methode fur singulär gestörte elliptische Randwertaufgaben, Dissertation, Techn. Hochschule Magdeburg 1986.
  20. G. I. SHISHKIN, 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: 851752] [Zbl: 0622.65078]
  21. G. I. SHISHKIN, V. A. TITOV, 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: 455427]

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