An equilibrium finite element method in three-dimensional elasticity

Křížek, 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 -