# An equilibrium finite element method in three-dimensional elasticity

Aplikace matematiky (1982)

- Volume: 27, Issue: 1, page 46-75
- ISSN: 0862-7940

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topKřížek, Michal. "An equilibrium finite element method in three-dimensional elasticity." Aplikace matematiky 27.1 (1982): 46-75. <http://eudml.org/doc/15223>.

@article{Křížek1982,

abstract = {The tetrahedral stress element is introduced and two different types of a finite piecewise linear approximation of the dual elasticity problem are investigated on a polyhedral domain. Fot both types a priori error estimates $O(h^2)$ in $L_2$-norm and $O(h^\{1/2\})$ in $L_\infty $-norm are established, provided the solution is smooth enough. These estimates are based on the fact that for any polyhedron there exists a strongly regular family of decomprositions into tetrahedra, which is proved in the paper, too.},

author = {Křížek, Michal},

journal = {Aplikace matematiky},

keywords = {composite tetrahedral equilibrium element; two types of finite approximation; three-dimensional problem; polyhedral domain; Castigliano-Menabrea’s principle; minimum complementary energy; a priori error estimates; existence of strongly regular family of decompositions; composite tetrahedral equilibrium element; two types of finite approximation; three-dimensional problem; polyhedral domain; Castigliano- Menabrea's principle; minimum complementary energy; a priori error estimates; existence of strongly regular family of decompositions},

language = {eng},

number = {1},

pages = {46-75},

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

title = {An equilibrium finite element method in three-dimensional elasticity},

url = {http://eudml.org/doc/15223},

volume = {27},

year = {1982},

}

TY - JOUR

AU - Křížek, Michal

TI - An equilibrium finite element method in three-dimensional elasticity

JO - Aplikace matematiky

PY - 1982

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

VL - 27

IS - 1

SP - 46

EP - 75

AB - The tetrahedral stress element is introduced and two different types of a finite piecewise linear approximation of the dual elasticity problem are investigated on a polyhedral domain. Fot both types a priori error estimates $O(h^2)$ in $L_2$-norm and $O(h^{1/2})$ in $L_\infty $-norm are established, provided the solution is smooth enough. These estimates are based on the fact that for any polyhedron there exists a strongly regular family of decomprositions into tetrahedra, which is proved in the paper, too.

LA - eng

KW - composite tetrahedral equilibrium element; two types of finite approximation; three-dimensional problem; polyhedral domain; Castigliano-Menabrea’s principle; minimum complementary energy; a priori error estimates; existence of strongly regular family of decompositions; composite tetrahedral equilibrium element; two types of finite approximation; three-dimensional problem; polyhedral domain; Castigliano- Menabrea's principle; minimum complementary energy; a priori error estimates; existence of strongly regular family of decompositions

UR - http://eudml.org/doc/15223

ER -

## References

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- I. Hlaváček J. Nečas, Mathematical theory of elastic and elasto-plastic bodies, SNTL, Praha, Elsevier, Amsterdam, 1980. (1980)
- I. Hlaváček, Convergence of an equilibrium finite element model for plane elastostatics, Apl. Mat. 24 (1979), 427-457. (1979) MR0547046
- C. Johnson B. Mercier, 10.1007/BF01403910, Numer. Math. 30 (1978), 103-116. (1978) MR0483904DOI10.1007/BF01403910
- J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Praha, 1967. (1967) MR0227584
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