Finite element analysis of primal and dual variational formulations of semicoercive elliptic problems with nonhomogeneous obstacles on the boundary

Tran, Van Bon. "Finite element analysis of primal and dual variational formulations of semicoercive elliptic problems with nonhomogeneous obstacles on the boundary." Aplikace matematiky 33.1 (1988): 1-21. <http://eudml.org/doc/15519>.

@article{Tran1988,
abstract = {The Poisson equation with non-homogeneous unilateral condition on the boundary is solved by means of finite elements. The primal variational problem is approximated on the basis of linear triangular elements, and $O(h)$-convergence is proved provided the exact solution is regular enough. For the dual problem piecewise linear divergence-free approximations are employed and $O(h^\{3/2\})$-convergence proved for a regular solution. Some a posteriori error estimates are also presented.},
author = {Tran, Van Bon},
journal = {Aplikace matematiky},
keywords = {semi-coercive elliptic problems; Poisson equation; finite elements; convergence; dual problem; a posteriori error estimates; variational inequalities; semi-coercive elliptic problems; Poisson equation; finite elements; convergence; dual problem; a posteriori error estimates},
language = {eng},
number = {1},
pages = {1-21},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finite element analysis of primal and dual variational formulations of semicoercive elliptic problems with nonhomogeneous obstacles on the boundary},
url = {http://eudml.org/doc/15519},
volume = {33},
year = {1988},
}

TY - JOUR
AU - Tran, Van Bon
TI - Finite element analysis of primal and dual variational formulations of semicoercive elliptic problems with nonhomogeneous obstacles on the boundary
JO - Aplikace matematiky
PY - 1988
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 33
IS - 1
SP - 1
EP - 21
AB - The Poisson equation with non-homogeneous unilateral condition on the boundary is solved by means of finite elements. The primal variational problem is approximated on the basis of linear triangular elements, and $O(h)$-convergence is proved provided the exact solution is regular enough. For the dual problem piecewise linear divergence-free approximations are employed and $O(h^{3/2})$-convergence proved for a regular solution. Some a posteriori error estimates are also presented.
LA - eng
KW - semi-coercive elliptic problems; Poisson equation; finite elements; convergence; dual problem; a posteriori error estimates; variational inequalities; semi-coercive elliptic problems; Poisson equation; finite elements; convergence; dual problem; a posteriori error estimates
UR - http://eudml.org/doc/15519
ER -