# The finite element solution of parabolic equations

Aplikace matematiky (1978)

- Volume: 23, Issue: 6, page 408-438
- ISSN: 0862-7940

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topNedoma, Josef. "The finite element solution of parabolic equations." Aplikace matematiky 23.6 (1978): 408-438. <http://eudml.org/doc/15071>.

@article{Nedoma1978,

abstract = {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.},

author = {Nedoma, Josef},

journal = {Aplikace matematiky},

keywords = {error bounds; approximate solutions; parabolic equations; arbitrary curved domains; quadrature formulas; optimal order of convergence; error bounds; approximate solutions; parabolic equations; arbitrary curved domains; quadrature formulas; optimal order of convergence},

language = {eng},

number = {6},

pages = {408-438},

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

title = {The finite element solution of parabolic equations},

url = {http://eudml.org/doc/15071},

volume = {23},

year = {1978},

}

TY - JOUR

AU - Nedoma, Josef

TI - The finite element solution of parabolic equations

JO - Aplikace matematiky

PY - 1978

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

VL - 23

IS - 6

SP - 408

EP - 438

AB - 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.

LA - eng

KW - error bounds; approximate solutions; parabolic equations; arbitrary curved domains; quadrature formulas; optimal order of convergence; error bounds; approximate solutions; parabolic equations; arbitrary curved domains; quadrature formulas; optimal order of convergence

UR - http://eudml.org/doc/15071

ER -

## References

top- 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. (1972) Zbl0262.65070MR0421108
- 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. (1972) Zbl0293.65086MR0345428
- Jindřich Nečas, Les Méthodes Directe en Théorie des Equations Elliptiques, Mason. Paris. 1967. (1967) MR0227584
- V. J. Smirnov, Kurs vyššej matěmatiki, tom V. Gosudarstvěnnoje izdatělstvo fiziko-matěmatičeskoj litěratury. Moskva. 1960. (1960)
- Miloš Zlámal, 10.1090/S0025-5718-1975-0371105-2, Mathematics of Computation, 29, Nr 130 (1975), 350-359. (1975) Zbl0302.65081MR0371105DOI10.1090/S0025-5718-1975-0371105-2
- Miloš Zlámal, 10.1137/0710022, SIAM J. Numer. Anal., 10. No 1 (1973), 229-240. (1973) Zbl0285.65067MR0395263DOI10.1137/0710022
- Miloš Zlámal, 10.1137/0711031, SIAM J. Numer. Anal., 11. No 2 (1974), 347-362. (1974) Zbl0277.65064MR0343660DOI10.1137/0711031
- Miloš Zlámal, 10.1090/S0025-5718-1974-0388813-9, Mathematics of Computation, 28, No 126 (1974), 393-404. (1974) Zbl0296.65054MR0388813DOI10.1090/S0025-5718-1974-0388813-9
- T. Dupont G. Fairweather J. P. Johnson, Three-level Galerkin Methods for Parabolic Equations, SIAM J. Numer. Anal., 11, No 2 (1974). (1974) Zbl0313.65107MR0403259
- M. Lees, 10.1215/S0012-7094-60-02727-7, Duke Math. J., 27 (1960), 287-311. (1960) Zbl0092.32803MR0121998DOI10.1215/S0012-7094-60-02727-7
- Miloš Zlámal, Finite element methods for nonlinear parabolic equations, R.A.I.R.O. Analyse numérique/Numerical Analysis, 11, No 1 (1977), 93-107. (1977) Zbl0385.65049MR0502073
- W. Liniger, 10.1007/BF02235394, Computing, 3 (1968), 280-285. (1968) Zbl0169.19902MR0239763DOI10.1007/BF02235394

## Citations in EuDML Documents

top- M. Vanmaele, A. Ženíšek, External finite element approximations of eigenvalue problems
- Josef Nedoma, The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements
- Alexander Ženíšek, Finite element methods for coupled thermoelasticity and coupled consolidation of clay
- Libor Čermák, The finite element solution of second order elliptic problems with the Newton boundary condition
- Helena Růžičková, Alexander Ženíšek, Finite elements methods for solving viscoelastic thin plates

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