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Keywords:
elliptic model problem; dual variational formulation; piecewise linear finite elements; a priori error estimates; a posteriori error estimates; two-sided bounds
elliptic model problem; dual variational formulation; piecewise linear finite elements; a priori error estimates; a posteriori error estimates; two-sided bounds
Summary:
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.
References:
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[3] I. Hlaváček: Dual finite element analysis for unilateral boundary value problems. Aplikace matematiky 22 (1977), 14-51. MR 0426453
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[5] U. Mosco G. Strang: One-sided approximations and variational inequalities. Bull. Am. Soc. 80 (1974), 308-312. DOI 10.1090/S0002-9904-1974-13477-4 | MR 0331818
[6] I. Hlaváček: Some equilibrium and mixed models in the finite element method. Proceedings of the Banach Internat. Math. Center, Warsaw (to appear). MR 0514379
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