| Title:
|
Grid adjustment based on a posteriori error estimators (English) |
| Author:
|
Segeth, Karel |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
38 |
| Issue:
|
6 |
| Year:
|
1993 |
| Pages:
|
488-504 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
grid adjustment |
| Keyword:
|
principle of equidistribution of monitor |
| Keyword:
|
a posteriori error estimate |
| Keyword:
|
parabolic equation |
| Keyword:
|
finite element method |
| Keyword:
|
method of lines |
| MSC:
|
35K15 |
| MSC:
|
65M15 |
| MSC:
|
65M20 |
| MSC:
|
65M50 |
| MSC:
|
65M60 |
| idZBL:
|
Zbl 0797.65068 |
| idMR:
|
MR1241452 |
| DOI:
|
10.21136/AM.1993.104571 |
| . |
| Date available:
|
2008-05-20T18:46:42Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104571 |
| . |
| Reference:
|
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| Reference:
|
[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 1217436 |
| Reference:
|
[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. MR 0845412, 10.1016/0045-7825(86)90084-8 |
| Reference:
|
[4] I. Babuška W.C. Rheinboldt: A-posteriori error estimates for the finite element method.Internat. J. Numer. Methods Engrg. 12 (1978), 1597-1615. 10.1002/nme.1620121010 |
| Reference:
|
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| Reference:
|
[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. MR 1067050, 10.1016/0021-9991(90)90148-T |
| Reference:
|
[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. MR 0729241, 10.1016/0377-0427(83)90009-2 |
| Reference:
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[8] A. C. Hindmarsh: LSODE and LSODI, two new initial value ordinary differential equation solvers.ACM SIGNUM Newsletter 15 (1980), 10-11. 10.1145/1218052.1218054 |
| Reference:
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[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 1195582 |
| Reference:
|
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| Reference:
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| Reference:
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[12] J. T. Oden G. F. Carey: Finite Elements: Mathematical Aspects, Vol. IV.Englewood Cliffs, NJ, Prentice-Hall, 1983. MR 0767806 |
| Reference:
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[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 0751605 |
| Reference:
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[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 1185646 |
| Reference:
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[15] V. Thomée: Negative norm estimates and superconvergence in Galerkin methods for parabolic problems.Math. Соmр. 34 (1980), 93-113. MR 0551292 |
| Reference:
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| . |
