| Title:
|
The finite element solution of parabolic equations (English) |
| Author:
|
Nedoma, Josef |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
23 |
| Issue:
|
6 |
| Year:
|
1978 |
| Pages:
|
408-438 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
In contradistinction to former results, the error bounds introduced in this paper are given for fully discretized approximate soltuions of parabolic equations and for arbitrary curved domains. Simplicial isoparametric elements in $n$-dimensional space are applied. Degrees of accuracy of quadrature formulas are determined so that numerical integration does not worsen the optimal order of convergence in $L_2$-norm of the method. (English) |
| Keyword:
|
error bounds |
| Keyword:
|
approximate solutions |
| Keyword:
|
parabolic equations |
| Keyword:
|
arbitrary curved domains |
| Keyword:
|
quadrature formulas |
| Keyword:
|
optimal order of convergence |
| MSC:
|
35K60 |
| MSC:
|
65N15 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0427.65075 |
| idMR:
|
MR0508545 |
| DOI:
|
10.21136/AM.1978.103769 |
| . |
| Date available:
|
2008-05-20T18:10:34Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103769 |
| . |
| Reference:
|
[1] P. G. Ciarlet, A. P. Raviart: The combined effect of curved boundaries and numerical integration in isoparametric finite element methods.In A. K. Aziz: The mathematical foundations of the finite element method with applications to partial differential equations. Academic Press. New York and London. 1972. Zbl 0262.65070, MR 0421108 |
| Reference:
|
[2] P. A. Raviart: The use of numerical integration in finite element methods for solving parabolic equations.Lecture presented at the Conference on Numerical Analysis. Royal Irish Academy. Dublin, August 14-18, 1972. MR 0345428 |
| Reference:
|
[3] Jindřich Nečas: Les Méthodes Directe en Théorie des Equations Elliptiques.Mason. Paris. 1967. MR 0227584 |
| Reference:
|
[4] V. J. Smirnov: Kurs vyššej matěmatiki.tom V. Gosudarstvěnnoje izdatělstvo fiziko-matěmatičeskoj litěratury. Moskva. 1960. |
| Reference:
|
[5] Miloš Zlámal: Finite Element Multistep Discretizations of Parabolic Boundary Value Problems.Mathematics of Computation, 29, Nr 130 (1975), 350-359. MR 0371105, 10.1090/S0025-5718-1975-0371105-2 |
| Reference:
|
[6] Miloš Zlámal: Curved Elements in the Finite Element Method I.SIAM J. Numer. Anal., 10. No 1 (1973), 229-240. MR 0395263, 10.1137/0710022 |
| Reference:
|
[7] Miloš Zlámal: Curved Elements in the Finite Element Methods II.SIAM J. Numer. Anal., 11. No 2 (1974), 347-362. MR 0343660, 10.1137/0711031 |
| Reference:
|
[8] Miloš Zlámal: Finite Element Methods for Parabolic Equations.Mathematics of Computation, 28, No 126 (1974), 393-404. MR 0388813, 10.1090/S0025-5718-1974-0388813-9 |
| Reference:
|
[9] T. Dupont G. Fairweather J. P. Johnson: Three-level Galerkin Methods for Parabolic Equations.SIAM J. Numer. Anal., 11, No 2 (1974). MR 0403259 |
| Reference:
|
[10] M. Lees: A priori estimates for the solutions of difference approximations to parabolic differential equations.Duke Math. J., 27 (1960), 287-311. MR 0121998, 10.1215/S0012-7094-60-02727-7 |
| Reference:
|
[11] Miloš Zlámal: Finite element methods for nonlinear parabolic equations.R.A.I.R.O. Analyse numérique/Numerical Analysis, 11, No 1 (1977), 93-107. MR 0502073 |
| Reference:
|
[12] W. Liniger: A criterion for A-stability of linear multistep integration formulae.Computing, 3 (1968), 280-285. Zbl 0169.19902, MR 0239763, 10.1007/BF02235394 |
| . |
