| Title:
|
A posteriori error estimates for parabolic differential systems solved by the finite element method of lines (English) |
| Author:
|
Segeth, Karel |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
39 |
| Issue:
|
6 |
| Year:
|
1994 |
| Pages:
|
415-443 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
a posteriori error estimate |
| Keyword:
|
system of parabolic equations |
| Keyword:
|
finite element method |
| Keyword:
|
method of lines |
| MSC:
|
35K15 |
| MSC:
|
65M15 |
| MSC:
|
65M20 |
| idZBL:
|
Zbl 0822.65068 |
| idMR:
|
MR1298731 |
| DOI:
|
10.21136/AM.1994.134269 |
| . |
| Date available:
|
2009-09-22T17:45:33Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134269 |
| . |
| Reference:
|
[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. MR 0849282, 10.1137/0723050 |
| 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.Numer. Math. 65 (1993), 1–21. MR 1217436, 10.1007/BF01385737 |
| Reference:
|
[3] 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:
|
[4] M. Bieterman, I. Babuška: The finite element method for parabolic equations I, II.Numer. Math. 40 (1982), 339–371, 373–406. 10.1007/BF01396451 |
| Reference:
|
[5] F.R. Gantmacher: Matrix Theory.Moskva, Nauka, 1966. (Russian) |
| Reference:
|
[6] 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:
|
[7] J.T. Oden, G.F. Carey: Finite Elements: Mathematical Aspects, Vol. 4.Englewood Cliffs, NJ, Prentice-Hall, 1983. MR 0767804 |
| Reference:
|
[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 0751605 |
| Reference:
|
[9] B. Szabo, I. Babuška: Finite Element Analysis.New York, J. Wiley & Sons, 1991. MR 1164869 |
| Reference:
|
[10] V. Thomée: Negative norm estimates and superconvergence in Galerkin methods for parabolic problems.Math. Comp. 34 (1980), 93–113. MR 0551292, 10.2307/2006222 |
| Reference:
|
[11] R. Wait, A.R. Mitchell: Finite Element Analysis and Applications.Chichester, J. Wiley & Sons, 1985. MR 0817440 |
| . |
