| Title:
|
Convergence of a finite element method based on the dual variational formulation (English) |
| Author:
|
Haslinger, Jaroslav |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
21 |
| Issue:
|
1 |
| Year:
|
1976 |
| Pages:
|
43-65 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
An "equilibrium model" with piecewise linear polynomials on triangular clements applied to the solution of a mixed boundary value problem for a second order elliptic equation is studied.
The procedure is proved to be second order correct in $h$ (the maximal side in the triangulation) provided the exact solution is sufficiently smooth. () |
| MSC:
|
35A35 |
| MSC:
|
35B45 |
| MSC:
|
35J20 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0326.35020 |
| idMR:
|
MR0398126 |
| DOI:
|
10.21136/AM.1976.103621 |
| . |
| Date available:
|
2008-05-20T18:03:24Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103621 |
| . |
| Reference:
|
[1] B. Fraeijs de Veubeke: Displacement and equilibrium models in the finite element method.Stress Analysis, ed. by O.C. Zienkiewicz and G. Holister, J. Wiley, 1965, 145-197. |
| Reference:
|
[2] B. Fraeijs de Veubeke O. C. Zienkiewicz: Strain energy bounds in finite-element analysis by slab analogies.J. Strain Analysis 2, (1967) 265 - 271. 10.1243/03093247V024265 |
| Reference:
|
[3] V. B., Jr. Watwood B. J. Hartz: An equilibrium stress field model for finite element solution of two-dimensional elastostatic problems.Int. J. Solids Structures 4, (1968), 857-873. 10.1016/0020-7683(68)90083-8 |
| Reference:
|
[4] B. Fraeijs de Veubeke M. Hogge: Dual analysis for heat conduction problems by finite elements.Int. J. Numer. Meth. Eng. 5, (1972), 65 - 82. 10.1002/nme.1620050107 |
| Reference:
|
[5] J. P. Aubin H. G. Burchard: Some aspects of the method of the hypercircle applied to elliptic variational problems.Numer. sol. Part. Dif. Eqs. II, SYNSPADE (1970), 1 - 67. MR 0285136 |
| Reference:
|
[6] J. Vacek: Dual variational principles for an elliptic partial differential equation.Apl. mat. 21 (1976), 5-27. Zbl 0345.35035, MR 0412594 |
| Reference:
|
[7] I. Hlaváček: On a conjugate semi-variational method for parabolic equations.Apl. mat. 18 (1973), 434-444. MR 0404858 |
| Reference:
|
[8] F. Grenacher: A posteriori error estimates for elliptic partial differential equations.Inst. Fluid Dynamics and Appl. Math., Univ. Maryland, TN-BN-T 43, July 1972. |
| Reference:
|
[9] W. Prager J. L. Synge: Approximations in elasticity based on the concept of function space.Quart. Appl. Math. 5 (1947), 241 - 269. MR 0025902, 10.1090/qam/25902 |
| Reference:
|
[10] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584 |
| Reference:
|
[11] I. Hlaváček: Variational principles in the linear theory of elasticity for general boundary conditions.Apl. mat. 12 (1967), 425-448. MR 0231575 |
| Reference:
|
[12] J. Haslinger J. Hlaváček: Convergence of a dual finite element method in $R_n$.CMUC 16 (1975), 469-485. MR 0386303 |
| Reference:
|
[13] H. Gajewski: On conjugate evolution equations and a posteriori error estimates.Proceedings of Internal. Summer School on Nonlinear Operators held in Berlin, 1975. |
| . |
