# Grid adjustment based on a posteriori error estimators

Applications of Mathematics (1993)

- Volume: 38, Issue: 6, page 488-504
- ISSN: 0862-7940

## Access Full Article

top## Abstract

top## How to cite

topSegeth, Karel. "Grid adjustment based on a posteriori error estimators." Applications of Mathematics 38.6 (1993): 488-504. <http://eudml.org/doc/15769>.

@article{Segeth1993,

abstract = {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.},

author = {Segeth, Karel},

journal = {Applications of Mathematics},

keywords = {grid adjustment; principle of equidistribution of monitor; a posteriori error estimate; parabolic equation; finite element method; method of lines; grid adjustment; finite element method of lines; error estimators; parabolic systems},

language = {eng},

number = {6},

pages = {488-504},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Grid adjustment based on a posteriori error estimators},

url = {http://eudml.org/doc/15769},

volume = {38},

year = {1993},

}

TY - JOUR

AU - Segeth, Karel

TI - Grid adjustment based on a posteriori error estimators

JO - Applications of Mathematics

PY - 1993

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 38

IS - 6

SP - 488

EP - 504

AB - 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.

LA - eng

KW - grid adjustment; principle of equidistribution of monitor; a posteriori error estimate; parabolic equation; finite element method; method of lines; grid adjustment; finite element method of lines; error estimators; parabolic systems

UR - http://eudml.org/doc/15769

ER -

## References

top- S. Adjerid J. E. Flaherty, 10.1137/0723050, SIAM J. Numer. Anal. 23 (1986), 778-796. (1986) MR0849282DOI10.1137/0723050
- 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. (1991) MR1217436
- I. Babuška W. Gui, 10.1016/0045-7825(86)90084-8, Comput. Methods Appl. Mech. Engrg. 55 (1986), 27-42. (1986) MR0845412DOI10.1016/0045-7825(86)90084-8
- I. Babuška W.C. Rheinboldt, 10.1002/nme.1620121010, Internat. J. Numer. Methods Engrg. 12 (1978), 1597-1615. (1978) DOI10.1002/nme.1620121010
- M. Bieterman I. Babuška, 10.1016/0021-9991(86)90083-5, J. Comput. Phys. 63 (1986), 33-66. (1986) MR0832563DOI10.1016/0021-9991(86)90083-5
- R. M. Furzeland J. G. Verwer P. A. Zegeling, 10.1016/0021-9991(90)90148-T, J. Comput. Phys. 89 (1990), 349-388. (1990) MR1067050DOI10.1016/0021-9991(90)90148-T
- B. M. Herbst S. W. Schoombie A. R. Mitchell, 10.1016/0377-0427(83)90009-2, J. Comput. Appl. Math. 9 (1983), 377-389. (1983) MR0729241DOI10.1016/0377-0427(83)90009-2
- A. C. Hindmarsh, 10.1145/1218052.1218054, ACM SIGNUM Newsletter 15 (1980), 10-11. (1980) DOI10.1145/1218052.1218054
- 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. (1992) MR1195582
- K. Miller, 10.1137/0718071, SIAM J. Numer. Anal. 18 (1981), 1033-1057. (1981) Zbl0518.65083MR0638997DOI10.1137/0718071
- K. Miller R. N. Miller, 10.1137/0718070, SIAM J. Numer. Anal. 18 (1981), 1019-1032. (1981) MR0638996DOI10.1137/0718070
- J. T. Oden G. F. Carey, Finite Elements: Mathematical Aspects, Vol. IV, Englewood Cliffs, NJ, Prentice-Hall, 1983. (1983) MR0767806
- L. R. Petzold, A Description of DDASSL: A Differential/Algebraic System Solver, Sandia Report No. Sand 82-8637, Livermore, CA, Sandia National Laboratory, 1982. (1982) MR0751605
- 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. (1989) MR1185646
- V. Thomée, Negative norm estimates and superconvergence in Galerkin methods for parabolic problems, Math. Соmр. 34 (1980), 93-113. (1980) MR0551292
- R. Wait A. R. Mitchell, Finite Element Analysis and Applications, Chichester, J. Wiley and Sons, 1985. (1985) MR0817440

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.