The finite element solution of second order elliptic problems with the Newton boundary condition

Libor Čermák

Aplikace matematiky (1983)

  • Volume: 28, Issue: 6, page 430-456
  • ISSN: 0862-7940

Abstract

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The convergence of the finite element solution for the second order elliptic problem in the n -dimensional bounded domain ( n ≥ 2 ) with the Newton boundary condition is analysed. The simplicial isoparametric elements are used. The error estimates in both the H 1 and L 2 norms are obtained.

How to cite

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Čermák, Libor. "The finite element solution of second order elliptic problems with the Newton boundary condition." Aplikace matematiky 28.6 (1983): 430-456. <http://eudml.org/doc/15322>.

@article{Čermák1983,
abstract = {The convergence of the finite element solution for the second order elliptic problem in the $n$-dimensional bounded domain $(n\ge 2)$ with the Newton boundary condition is analysed. The simplicial isoparametric elements are used. The error estimates in both the $H^1$ and $L_2$ norms are obtained.},
author = {Čermák, Libor},
journal = {Aplikace matematiky},
keywords = {convergence; finite element; Newton boundary condition; simplicial isoparametric elements; error estimates; convergence; finite element; Newton boundary condition; simplicial isoparametric elements; error estimates},
language = {eng},
number = {6},
pages = {430-456},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The finite element solution of second order elliptic problems with the Newton boundary condition},
url = {http://eudml.org/doc/15322},
volume = {28},
year = {1983},
}

TY - JOUR
AU - Čermák, Libor
TI - The finite element solution of second order elliptic problems with the Newton boundary condition
JO - Aplikace matematiky
PY - 1983
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 28
IS - 6
SP - 430
EP - 456
AB - The convergence of the finite element solution for the second order elliptic problem in the $n$-dimensional bounded domain $(n\ge 2)$ with the Newton boundary condition is analysed. The simplicial isoparametric elements are used. The error estimates in both the $H^1$ and $L_2$ norms are obtained.
LA - eng
KW - convergence; finite element; Newton boundary condition; simplicial isoparametric elements; error estimates; convergence; finite element; Newton boundary condition; simplicial isoparametric elements; error estimates
UR - http://eudml.org/doc/15322
ER -

References

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  2. P. G. Ciarlet P. A. Raviart, The combined effect of curved boundaries and numerical integration in isoparametric finite element methods, In: The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz Editor). Academic Press. New York and London. 1972. (1972) MR0421108
  3. A. Kufner O. John S. Fučík, Function Spaces, Academia. Praha, 1977. (1977) MR0482102
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  6. J. Nedoma, The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements, R.A.I.R.O. Numer. Anal., 13 (1979), 257-289. (1979) Zbl0413.65080MR0543935
  7. K. Rektorys, Variační metody, SNTL. Praha. 1974. English translation: Variational Methods. Reidel Co.. Dordrecht-Boston. 1977. (1974) Zbl0371.35001MR0487653
  8. R. Scott, 10.1137/0712032, SIAM J. Numer. Anal., 12 (1975), 404-427. (1975) Zbl0357.65082MR0386304DOI10.1137/0712032
  9. G. Strang, 10.1007/BF01395933, Numer. Math., 19 (1972), 81-98. (1972) Zbl0221.65174MR0305547DOI10.1007/BF01395933
  10. M. Zlámal, 10.1137/0710022, SIAM J. Numer. Anal., 10 (1973), 229-240. (1973) MR0395263DOI10.1137/0710022
  11. M. Zlámal, 10.1137/0711031, SIAM J. Numer. Anal., 11 (1974), 347-369. (1974) MR0343660DOI10.1137/0711031
  12. A. Ženíšek, Nonhomogeneous boundary conditions and curved triangular finite elements, Apl. Mat., 26 (1981), 121-141. (1981) MR0612669
  13. A. Ženíšek, Discrete forms of Friedrichs' inequalities in the finite element method, R.A.I.R.O. Numer. Anal., 15 (1981), 265-286. (1981) Zbl0475.65072MR0631681

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