Geodesic
On FE-grid relocation in solving unilateral boundary value problems by FEM
Applications of Mathematics, Tome 37 (1992) no. 2, pp. 105-122.

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We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions. Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the plane elasticity problem with unilateral boundary conditions are given. In plane elasticity we consider problems with and without friction.
DOI : 10.21136/AM.1992.104495
Classification : 35J05, 65N30, 65N50
Keywords: unilateral boundary value problem; grid relocation; finite element methods; Poisson equation; numerical examples; nonlinear optimization; sequential quadratic programming code; FE-grid relocation 
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     title = {On {FE-grid} relocation in solving unilateral boundary value problems by {FEM}},
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Haslinger, Jaroslav; Neittaanmäki, P.; Salmenjoki, K. On FE-grid relocation in solving unilateral boundary value problems by FEM. Applications of Mathematics, Tome 37 (1992) no. 2, pp. 105-122. doi : 10.21136/AM.1992.104495. http://geodesic.mathdoc.fr/articles/10.21136/AM.1992.104495/

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