A local L 2 -error analysis of the streamline diffusion method for nonstationary convection-diffusion systems
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 29 (1995) no. 5, p. 577-603
@article{M2AN_1995__29_5_577_0,
     author = {Zhou, Guohui},
     title = {A local $L^2$-error analysis of the streamline diffusion method for nonstationary convection-diffusion systems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {29},
     number = {5},
     year = {1995},
     pages = {577-603},
     zbl = {0839.65100},
     mrnumber = {1352863},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1995__29_5_577_0}
}
Zhou, Guohui. A local $L^2$-error analysis of the streamline diffusion method for nonstationary convection-diffusion systems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 29 (1995) no. 5, pp. 577-603. http://www.numdam.org/item/M2AN_1995__29_5_577_0/

[1] E. Eriksson, C. Johnson, Adaptive finite element methods for parabolic problems IV : Nonlinear problems, to appear. | Zbl 0835.65116

[2] E. Eriksson, C. Johnson, V. Thomée, Time discretization of parabolic problems by the discontinuous Galerkin method, Math. Modelling and Numer. Anal, 19, 1985, 611-643. | Numdam | MR 826227 | Zbl 0589.65070

[3] T. J. R. Hughes, M. Mallet, A. Mizukami, A new finite element formulation for computational fluid dynamics : II. Beyond SUPG, Comput. Methods Appl. Mech. Engrg., 54, 1986, 341-355. | MR 836189 | Zbl 0622.76074

[4] T. J. R. Hughes, M. Mallet, A new finite element formulation for computational fluid dynamics : III. The general streamline operator for multidimensional advective-diffusive Systems, Comput Methods Appl. Mech. Engrg., 58, 1986, 305-328. | MR 865671 | Zbl 0622.76075

[5] T. J. R. Hughes, M. Mallet, A new finite element formulation for computational fluid dynamics : IV. A discontinuity-capturing operator for multidimensional advective-diffusive Systems, Comput. Methods Appl. Mech. Engrg., 58, 1986, 329-336. | MR 865672 | Zbl 0587.76120

[6] C. Johnson, Finite element methods for convection-diffusion problems, in : Computing Methods in Engineering and Applied Sciences V, (R. Glowinski and J. L. Lions, eds.), North-Holland, 1981. | MR 784648 | Zbl 0505.76099

[7] C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge University Press, 1987. | MR 925005 | Zbl 0628.65098

[8] C. Johnson, U. Nävert, An analysis of some finite element methods for advection-diffusion, in Analytical and Numerical Approaches to Asymptotic Problems in Analysis, (O. Axelsson, L. S. Frank and A. van der Sluis, eds.), North-Holland, 1981. | MR 605494 | Zbl 0455.76081

[9] C. Johnson, U. Nävert, J. Pitkäranta, Finite element methods for linear hyperbolic problems, Comput. Methods Appl. Mech. Engrg., 45, 1984, 285-312. | MR 759811 | Zbl 0526.76087

[10] C. Johnson, A. H. Schatz, L. B. Wahlbin, Crosswind smear and pointwise errors in streamline diffusion finite element methods, Math. Comp., 49, 179, 1987, 25-38. | MR 890252 | Zbl 0629.65111

[11] U. Nävert, A finite element method for convection-diffusion problems, Thesis, Chalmers University of Technology, Göteborg, Sweden, 1982.

[12] R. Rannacher, G. Zhou, Mesh adaptation via a predictor-corrector strategy in the streamline diffusion method for nonstationary hyperbolic Systems. Proceedings of the 9th GAMM-Seminar Kiel, Eds. W. Hackbusch and G. Wittum, Vieweg Verlag Stuttgart, 1993. | Zbl 0808.65098

[13] L. R. Scott, S. Y. Zhang, Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions, Math. Comp., 54, 190, 1990, 483-493. | MR 1011446 | Zbl 0696.65007

[14] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer Heidelberg, 1983. | MR 688146 | Zbl 0508.35002

[15] G. Zhou, An adaptive streamline diffusion finite element method for hyperbolic Systems in gas dynamics, Thesis, Heidelberg University, Germany, 1992.

[16] G. Zhou, Local pointwise error estimates for the streamline diffusion method applied to nonstationary hyperbolic problems, SFB 359 Preprint 93-64, Heidelberg University, 1993. | MR 1359411 | Zbl 0837.65100

[17] G. Zhou, R. Rannacher, Mesh orientation and refinement in the streamline diffusion method, SFB 359 Preprint 93-57, Heidelberg University, 1993.