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Dual finite element analysis for some elliptic variational equations and inequalities

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Abstract

In some boundary-value problems the gradient or the cogradient of the solution is more important than the solution itself. Dual variational formulation of elliptic problems is utilized to define finiteelement approximations of the cogradient. A priori error estimates are presented for a class of second-order elliptic problems, including problems of elastostatics.

If the boundary conditions are classical (i.e., of Dirichlet, Neumann. Newton, or mixed type), the primal and dual formulations are equivalent with variational equations, whereas the unilateral boundary conditions lead to variational inequalities. The paper has a surveyable character.

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  1. Mathematical Institute of the Czechoslovak Academy of Sciences, Prague, Czechoslovakia

    Ivan Hlaváček

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  1. Ivan Hlaváček
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Hlaváček, I. Dual finite element analysis for some elliptic variational equations and inequalities. Acta Appl Math 1, 121–150 (1983). https://doi.org/10.1007/BF00046832

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  • DOI: https://doi.org/10.1007/BF00046832

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