Geodesic
Grid adjustment based on a posteriori error estimators
Applications of Mathematics, Tome 38 (1993) no. 6, pp. 488-504
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The adjustment of one-dimensional space grid for a parabolic partial differential equation solved by the finite element method of lines is considered in the paper. In particular, the approach based on a posteriori error indicators and error estimators is studied. A statement on the rate of convergence of the approximation of error by estimator to the error in the case of a system of parabolic equations is presented.
The adjustment of one-dimensional space grid for a parabolic partial differential equation solved by the finite element method of lines is considered in the paper. In particular, the approach based on a posteriori error indicators and error estimators is studied. A statement on the rate of convergence of the approximation of error by estimator to the error in the case of a system of parabolic equations is presented.
DOI : 10.21136/AM.1993.104571
Classification : 35K15, 65M15, 65M20, 65M50, 65M60
Keywords: grid adjustment; principle of equidistribution of monitor; a posteriori error estimate; parabolic equation; finite element method; method of lines 
@article{10_21136_AM_1993_104571,
     author = {Segeth, Karel},
     title = {Grid adjustment based on a posteriori error estimators},
     journal = {Applications of Mathematics},
     pages = {488--504},
     year = {1993},
     volume = {38},
     number = {6},
     doi = {10.21136/AM.1993.104571},
     mrnumber = {1241452},
     zbl = {0797.65068},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1993.104571/}
}
TY  - JOUR
AU  - Segeth, Karel
TI  - Grid adjustment based on a posteriori error estimators
JO  - Applications of Mathematics
PY  - 1993
SP  - 488
EP  - 504
VL  - 38
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1993.104571/
DO  - 10.21136/AM.1993.104571
LA  - en
ID  - 10_21136_AM_1993_104571
ER  - 
%0 Journal Article
%A Segeth, Karel
%T Grid adjustment based on a posteriori error estimators
%J Applications of Mathematics
%D 1993
%P 488-504
%V 38
%N 6
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1993.104571/
%R 10.21136/AM.1993.104571
%G en
%F 10_21136_AM_1993_104571
Segeth, Karel. Grid adjustment based on a posteriori error estimators. Applications of Mathematics, Tome 38 (1993) no. 6, pp. 488-504. doi: 10.21136/AM.1993.104571

[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. Tech. Report 91-1, Troy, NY, Dept. of Computer Science, Rensselaer Polytechnic Institute, 1991. | MR

[3] I. Babuška W. Gui: Basic principles of feedback and adaptive approaches in the finite element method. Comput. Methods Appl. Mech. Engrg. 55 (1986), 27-42. | DOI | MR

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

[5] M. Bieterman I. Babuška: An adaptive method of lines with error control for parabolic equations of the reaction-diffusion type. J. Comput. Phys. 63 (1986), 33-66. | DOI | MR

[6] R. M. Furzeland J. G. Verwer P. A. Zegeling: A numerical study of three moving grid methods for one-dimensional partial differential equations which are based on the method of lines. J. Comput. Phys. 89 (1990), 349-388. | DOI | MR

[7] B. M. Herbst S. W. Schoombie A. R. Mitchell: Equidistributing principles in moving finite element methods. J. Comput. Appl. Math. 9 (1983), 377-389. | DOI | MR

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

[9] J. Hugger: Density Representation of Finite Element Meshes for One and Two Dimensional Problems, Non-Singular or with Point Singularities. Part 1 and 2, Preprint, College Park, MD, IPST, University of Maryland, 1992. | MR

[10] K. Miller: Moving finite elements II. SIAM J. Numer. Anal. 18 (1981), 1033-1057. | DOI | MR | Zbl

[11] K. Miller R. N. Miller: Moving finite elements I. SIAM J. Numer. Anal. 18 (1981), 1019-1032. | DOI | MR

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

[13] 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

[14] Y. Ren R. D. Russell: Moving Mesh Techniques Based upon Equidistribution, and Their Stability. Preprint, Burnaby, B.C., Dept. of Mathematics and Statistics, Simon Fraser University, 1989. | MR

[15] V. Thomée: Negative norm estimates and superconvergence in Galerkin methods for parabolic problems. Math. Соmр. 34 (1980), 93-113. | MR

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

Cité par Sources :