Geodesic
A posteriori error estimates for parabolic differential systems solved by the finite element method of lines
Applications of Mathematics, Tome 39 (1994) no. 6, pp. 415-443

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

DOI MR   Zbl

Systems of parabolic differential equations are studied in the paper. Two a posteriori error estimates for the approximate solution obtained by the finite element method of lines are presented. A statement on the rate of convergence of the approximation of error by estimator to the error is proved.
Systems of parabolic differential equations are studied in the paper. Two a posteriori error estimates for the approximate solution obtained by the finite element method of lines are presented. A statement on the rate of convergence of the approximation of error by estimator to the error is proved.
DOI : 10.21136/AM.1994.134269
Classification : 35K15, 65M15, 65M20
Keywords: a posteriori error estimate; system of parabolic equations; finite element method; method of lines 
Segeth, Karel. A posteriori error estimates for parabolic differential systems solved by the finite element method of lines. Applications of Mathematics, Tome 39 (1994) no. 6, pp. 415-443. doi: 10.21136/AM.1994.134269
@article{10_21136_AM_1994_134269,
     author = {Segeth, Karel},
     title = {A posteriori error estimates for parabolic differential systems solved by the finite element method of lines},
     journal = {Applications of Mathematics},
     pages = {415--443},
     year = {1994},
     volume = {39},
     number = {6},
     doi = {10.21136/AM.1994.134269},
     mrnumber = {1298731},
     zbl = {0822.65068},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134269/}
}
TY  - JOUR
AU  - Segeth, Karel
TI  - A posteriori error estimates for parabolic differential systems solved by the finite element method of lines
JO  - Applications of Mathematics
PY  - 1994
SP  - 415
EP  - 443
VL  - 39
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134269/
DO  - 10.21136/AM.1994.134269
LA  - en
ID  - 10_21136_AM_1994_134269
ER  - 
%0 Journal Article
%A Segeth, Karel
%T A posteriori error estimates for parabolic differential systems solved by the finite element method of lines
%J Applications of Mathematics
%D 1994
%P 415-443
%V 39
%N 6
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134269/
%R 10.21136/AM.1994.134269
%G en
%F 10_21136_AM_1994_134269

[1] S. Adjerid, J.E. Flaherty: A moving finite element method with error estimation and refinement for one-dimensional time dependent partial differential equations. SIAM J. Numer. Anal. 23 (1986), 778–796. | DOI | MR

[2] S. Adjerid, J.E. Flaherty, Y.J. Wang: A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems. Numer. Math. 65 (1993), 1–21. | DOI | MR

[3] I. Babuška, W.C. Rheinboldt: A posteriori error estimates for the finite element method. Internat. J. Numer. Methods Engrg. 12 (1978), 1597–1615. | DOI

[4] M. Bieterman, I. Babuška: The finite element method for parabolic equations I, II. Numer. Math. 40 (1982), 339–371, 373–406. | DOI

[5] F.R. Gantmacher: Matrix Theory. Moskva, Nauka, 1966. (Russian)

[6] A.C. Hindmarsh: LSODE and LSODI, two new initial value ordinary differential equation solvers. ACM SIGNUM Newsletter 15 (1980), 10–11. | DOI

[7] J.T. Oden, G.F. Carey: Finite Elements: Mathematical Aspects, Vol. 4. Englewood Cliffs, NJ, Prentice-Hall, 1983. | MR

[8] L.R. Petzold: A Description of DDASSL: A Differential/Algebraic System Solver. Sandia Report No. Sand 82-8637, Livermore, CA, Sandia National Laboratory, 1982. | MR

[9] B. Szabo, I. Babuška: Finite Element Analysis. New York, J. Wiley & Sons, 1991. | MR

[10] V. Thomée: Negative norm estimates and superconvergence in Galerkin methods for parabolic problems. Math. Comp. 34 (1980), 93–113. | DOI | MR

[11] R. Wait, A.R. Mitchell: Finite Element Analysis and Applications. Chichester, J. Wiley & Sons, 1985. | MR

Cité par Sources :