Ivan Hlaváček, Ján Lovíšek (1980)
Aplikace matematiky
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The plane Signorini problem is considered in the cases, when there exist non-trivial rigid admissible displacements. The existence and uniqueness of the solution and the convergence of piecewise linear finite element approximations is discussed.
María-Luisa Rapún, Francisco-Javier Sayas (2006)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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This paper proposes and analyzes a BEM-FEM scheme to approximate a time-harmonic diffusion problem in the plane with non-constant coefficients in a bounded area. The model is set as a Helmholtz transmission problem with adsorption and with non-constant coefficients in a bounded domain. We reformulate the problem as a four-field system. For the temperature and the heat flux we use piecewise constant functions and lowest order Raviart-Thomas elements associated to a triangulation approximating...
Patrick Hild (2002)
International Journal of Applied Mathematics and Computer Science
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We are interested in the finite element approximation of Coulomb's frictional unilateral contact problem in linear elasticity. Using a mixed finite element method and an appropriate regularization, it becomes possible to prove existence and uniqueness when the friction coefficient is less than Cε^{2}|log(h)|^{-1}, where h and ε denote the discretization and regularization parameters, respectively. This bound converging very slowly towards 0 when h decreases (in comparison with the already...
Vivette Girault, Larkin Ridgway Scott (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We propose and analyze several finite-element schemes for solving a grade-two fluid model, with a tangential boundary condition, in a two-dimensional polygon. The exact problem is split into a generalized Stokes problem and a transport equation, in such a way that it always has a solution without restriction on the shape of the domain and on the size of the data. The first scheme uses divergence-free discrete velocities and a centered discretization of the transport term, whereas the...
Ivan Hlaváček (1994)
Applications of Mathematics
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A model shape optimal design in is solved by means of the penalty method with extrapolation, which enables to obtain high order approximations of both the state function and the boundary flux, thus offering a reliable gradient for the sensitivity analysis. Convergence of the proposed method is proved for certain subsequences of approximate solutions.
Jaroslav Haslinger (1977)
Aplikace matematiky
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Finite element analysis of unilateral problems with obstacles on the boundary is given. Provided the exact solution is smooth enough, we obtain the rate of convergence for the case of one and two (lower and upper) obstacles on the boundary. At the end of this paper the proof of convergence without any regularity assumptions on the exact solution is given.