| Title:
|
Computation of derivatives in the finite element method (English) |
| Author:
|
Babuška, Ivo |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
11 |
| Issue:
|
3 |
| Year:
|
1970 |
| Pages:
|
545-558 |
| . |
| Category:
|
math |
| . |
| MSC:
|
65-66 |
| MSC:
|
65Jxx |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0219.65089 |
| idMR:
|
MR0275694 |
| . |
| Date available:
|
2008-06-05T20:33:14Z |
| Last updated:
|
2012-04-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/105297 |
| . |
| Reference:
|
[1] M. ZLÁMAL: On the finite element method.Num. Math. 12 (1968), 394-409. MR 0243753 |
| Reference:
|
[2] J. P. AUBIN: Behavior of the error of the approximate solutions of boundary value problems for linear elliptic operators by Galerkin's and finite difference methods.Ann. Scuola Norm. Pisa XXI (1967), 559-637. |
| Reference:
|
[3] P. G. CIARLET M. H. SCHULTZ R. S. VARGA: Numerical methods of high-order accuracy for nonlinear boundary value problems I. One dimens.Mum. Math. 9 (1967), 394-430. MR 0221761 |
| Reference:
|
[4] M. H. SCHULTZ: $L^2$ - multivariate approximation theory.SIAM J. Num. Anal. vol. 6, No. 2 (June 1969), 184-209. Zbl 0202.34901, MR 0251410 |
| Reference:
|
[5] M. H. SCHULTZ: $L^\infty$ -multivariate approximation theory.SIAM J. Num. Anal. vol. 6, no. 2 (June 1969), 161-183. Zbl 0202.34901, MR 0251409 |
| Reference:
|
[6] J. H. BRAMBLE M. ZLÁMAL: Triangular elements in the finite element method.To appear. Zbl 0276.65052, MR 0282540 |
| Reference:
|
[7] O. C. ZIENKIEWICZ: The finite element method in structural and continuum mechanics.London, McGraw Hill 1967. Zbl 0189.24902 |
| Reference:
|
[8] Y. R. RASHID: On computational methods in solid mechanics and stress analysis.Conf. on the Effective Use of Comp. in the nuclear industry April 21-23, 1969 Knowville. |
| Reference:
|
[9] L. A. OGANESJAN L. A. RUCHOVEC: Variational difference schemes for second order linear elliptic equations in a two dimensional region with a piecewise smooth boundary.(Russ.) Ž. Vyčisl. Mat. i Mat. Fiz. 8 (1968), 97-114. MR 0233525 |
| Reference:
|
[10] L. A. OGANESJAN L. A. RUCHOVEC: A study of the rates of convergence of some variational-difference schemes for elliptic equations of second order in a two dimensional domain with smooth boundary.(Russian.) Ž. Vyčisl. Mat. i Mat. Fiz. 9 (1969), 1102-1119. MR 0295599 |
| Reference:
|
[11] J. NITSCHE: Lineare Spline Funktionen und die Methode von Ritz für elliptische Randwertprobleme.To appear. MR 0255043 |
| Reference:
|
[12] I. BABUŠKA: Error-Bounds for finite element method.Tech. Note BN-630, University of Maryland, Institute for Fluid Dynamics and Applied Mathematics, November 1969. MR 0288971 |
| Reference:
|
[13] I. BABUŠKA: Numerical solution of boundary value problems by the perturbed variational principle.Tech. Note BN-624, University of Maryland, Institute for Fluid Dynamics and Applied Mathematics, October 1969. |
| Reference:
|
[14] I. BABUŠKA: The finite element method for elliptic equationa with discontinuous coefficients.Tech. Note BN-631, University of Maryland, Institute for Fluid. Dynamics and Applied Mathematics, Dec. 1969. |
| Reference:
|
[15] I. BABUŠKA: Finite element method for domains with corners.Tech. Note BN-636, University of Maryland, Inst. for Fluid Dynamics and Applied Mathematics, January 1970. |
| Reference:
|
[16] I. BABUŠKA: The rate of convergence for the finite element method.Technical Note BN-646, University of Maryland, Inst. for Fluid. Dynamics and Applied Mathematics, March 1970. MR 0287715 |
| Reference:
|
[17] I. BABUŠKA: Approximation by hill functions.Tech. Note BN-648, Univ. of Maryland, Inst. for Fluid Dynamics and Applied Mathematics, March 1970. |
| Reference:
|
[18] K. YOSIDA: Functional analysis.New York, Academic Press 1965. Zbl 0126.11504, MR 0180824 |
| Reference:
|
[19] I. M. GELFAND G. M. SHILOV: Generalized functions.(translated from Russian), Vol. 1, Vol. 2. Academic Press, New York - London. |
| Reference:
|
[20] J. SEGETHOVÁ: Numerical construction of the hill functions.Tech. Rep. 70-110-NGL-21-002-008, University of Maryland, Computer Science Center, April 1970. |
| Reference:
|
[21] H. ARONSZAJN: Boundary value of functions with finite Dirichlet integral.Conf. on Part. Diff. Equa. No. 14, University of Kansas 1955. |
| Reference:
|
[22] M. I. SLOBODECKIJ: Generalized Sobolev spaces and other application to boundary problems for partial differential equations.Leningrad. Gos. Univ. 97 (1958), 54-112. MR 0203222 |
| Reference:
|
[23] J. L. LIONS E. MAGENES: Problèmes aux limites non homogènes et applications.Vol. 1, Dunod 1968. MR 0247243 |
| Reference:
|
[24] E. STEIN: Lectures Notes.Orsay 66/67. |
| Reference:
|
[25] Jaok PEETRE: Applications de la théorie des espaces d'interpolation dans l'analyse harmonique.Ricerche Mat. 15 (1966), 3-36. MR 0221214 |
| . |
