Geodesic
Dual finite element analysis for elliptic problems with obstacles on the boundary. I
Applications of Mathematics, Tome 22 (1977) no. 4, pp. 244-255.

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For an elliptic model problem with non-homogeneous unilateral boundary conditions, two dual variational formulations are presented and justified on the basis of a saddle point theorem. Using piecewise linear finite element models on the triangulation of the given domain, dual numerical procedures are proposed. By means of one-sided approximations, some a priori error estimates are proved, assuming that the solution is sufficiently smooth. A posteriori error estimates and two-sided bounds for the energy are also deduced.
DOI : 10.21136/AM.1977.103701
Classification : 35J25, 65K10, 65N15, 65N30
Mots-clés : elliptic model problem; dual variational formulation; piecewise linear finite elements; a priori error estimates; a posteriori error estimates; two-sided bounds 
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     author = {Hlav\'a\v{c}ek, Ivan},
     title = {Dual finite element analysis for elliptic problems with obstacles on the boundary. {I}},
     journal = {Applications of Mathematics},
     pages = {244--255},
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     url = {https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1977.103701/}
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Hlaváček, Ivan. Dual finite element analysis for elliptic problems with obstacles on the boundary. I. Applications of Mathematics, Tome 22 (1977) no. 4, pp. 244-255. doi : 10.21136/AM.1977.103701. https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1977.103701/

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