Error estimates and step-size control for the approximate solution of a first order evolution equation
ESAIM: Modélisation mathématique et analyse numérique, Tome 25 (1991) no. 1, pp. 111-128.
@article{M2AN_1991__25_1_111_0,
     author = {Lippold, G\"unter},
     title = {Error estimates and step-size control for the approximate solution of a first order evolution equation},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {111--128},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {25},
     number = {1},
     year = {1991},
     mrnumber = {1086843},
     zbl = {0724.65065},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1991__25_1_111_0/}
}
TY  - JOUR
AU  - Lippold, Günter
TI  - Error estimates and step-size control for the approximate solution of a first order evolution equation
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1991
SP  - 111
EP  - 128
VL  - 25
IS  - 1
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://archive.numdam.org/item/M2AN_1991__25_1_111_0/
LA  - en
ID  - M2AN_1991__25_1_111_0
ER  - 
%0 Journal Article
%A Lippold, Günter
%T Error estimates and step-size control for the approximate solution of a first order evolution equation
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1991
%P 111-128
%V 25
%N 1
%I AFCET - Gauthier-Villars
%C Paris
%U http://archive.numdam.org/item/M2AN_1991__25_1_111_0/
%G en
%F M2AN_1991__25_1_111_0
Lippold, Günter. Error estimates and step-size control for the approximate solution of a first order evolution equation. ESAIM: Modélisation mathématique et analyse numérique, Tome 25 (1991) no. 1, pp. 111-128. http://archive.numdam.org/item/M2AN_1991__25_1_111_0/

[1] O. Axelsson, Error estimates over infinite intervals of some discretizations of evolution equations, BIT 24 (1984), 413-429 | MR | Zbl

[2] I. Babuška and W. C. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J Numer Anal 75 (1978), 736-754 | MR | Zbl

[3] M. Bietermann and I. Babuška, An adaptive method of lines with error control for parabolic equations of the reaction-diffusion type, J Comp Phys 63 (1986), 33-66 | MR | Zbl

[4] K. Ericsson, C. Johnson and V. Thomee, Time discretization of par abolie problems by the discontinuons Galerkin method, M2AN 19 (1985), 611-643 | Numdam | MR | Zbl

[5] H. Gajewski, K. Roger and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin, 1974 | MR | Zbl

[6] K. Groger, Discrete-time Galerkin methods for nonlinear evolution equations, Math Nachr 84 (1978), 247-275 | MR | Zbl

[7] C. Johnson, Y.-Y. Nie and V. Thomee, An a posteriori error estimate for a backward Euler discretization of a parabolic problem, SIAM J Numer Anal, 27 (1990), 277-291 | MR | Zbl

[8] J. Kačur, Method of Rothe in evolution equations, Teubner Leipzig, 1985 | MR | Zbl

[9] J. L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications I, Dunod, Paris, 1968 | Zbl

[10] G. Lippold, Adaptive approximation, ZAMM 67 (1987), 453-465 | MR | Zbl

[11] M. Luskin and R. Rannacher, On the smoothing property of the Galerkin method for par abolic equations, SIAM J Numer Anal 19 (1981), 93-113 | MR | Zbl

[12] J. Nečas, Application of Rothe's method to abstract parabohe equations, Czech Math J 24 (1974), 496-500 | EuDML | MR | Zbl

[13] P. A. Raviart, Sur l'approximation de certaines équations d'évolution linéaires et non linéaires, J Math Pures Appl 46 (1967), 11-107, 109-183 | Zbl

[14] Th. Reiher, An adaptive method for linear parabolic partial differential equations, ZAMM 67 (1987), 557-565 | MR | Zbl

[15] E. Rothe, Zweidimensionale parabolische Randwertaufgaben als Grenzfall eindimensionaler Randwertaufgaben, Math. Ann. 102 (1930), 650-670. | EuDML | JFM | MR

[16] J. M. Sanz-Serna and G. Verwer, Stability and convergence in the PDE/stiff ODE interphase, Report NM-R8619, Centre for Mathematics and Computer Science Amsterdam, 1986.

[17] V. Thomée andL. B. Wahlbin, On Galerkin methods in semilinear parabolic problems, SIAM J. Numer. Anal. 12 (1975), 378-389. | MR | Zbl

[18] M. F. Wheeler, An H-1 Galerkin method for a parabolic problem in a single space variable, SIAM J. Numer. Anal. 12 (1975), 803-817. | MR | Zbl