Geodesic
Optimization of the domain in elliptic problems by the dual finite element method
Applications of Mathematics, Tome 30 (1985) no. 1, pp. 50-72.

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An optimal part of the boundary of a plane domain for the Poisson equation with mixed boundary conditions is to be found. The cost functional is (i) the internal energy, (ii) the norm of the external flux through the unknown boundary. For the numerical solution of the state problem a dual variational formulation - in terms of the gradient of the solution - and spaces of divergence-free piecewise linear finite elements are used. The existence of an optimal domain and some convergence results are proved.
DOI : 10.21136/AM.1985.104126
Classification : 35J20, 35J25, 49D25, 65N30
Mots-clés : dual finite element method; optimal domain; Thomson principle; rate of convergence; numerical examples 
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     title = {Optimization of the domain in elliptic problems by the dual finite element method},
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Hlaváček, Ivan. Optimization of the domain in elliptic problems by the dual finite element method. Applications of Mathematics, Tome 30 (1985) no. 1, pp. 50-72. doi : 10.21136/AM.1985.104126. https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1985.104126/

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