On the accuracy of asymptotic approximations for longitudinal deformation of a thin plate
Localization effects for eigenfunctions near to the edge of a thin domain
It is proved that the first eigenfunction of the mixed boundary-value problem for the Laplacian in a thin domain is localized either at the whole lateral surface of the domain, or at a point of , while the eigenfunction decays exponentially inside . Other effects, attributed to the high-frequency range of the spectrum, are discussed for eigenfunctions of the mixed boundary-value and Neumann problems, too.
Optimal convergence results for the Brezzi-Pitkäranta approximation of the Stokes problem: Exterior domains
This paper deals with a strongly elliptic perturbation for the Stokes equation in exterior three-dimensional domains Ω with smooth boundary. The continuity equation is substituted by the equation -ε²Δp + div u = 0, and a Neumann boundary condition for the pressure is added. Using parameter dependent Sobolev norms, for bounded domains and for sufficiently smooth data we prove convergence for the velocity part and convergence for the pressure to the solution of the Stokes problem, with δ arbitrarily...
Selfadjoint Extensions for the Elasticity System in Shape Optimization
Two approaches are proposed to modelling of topological variations in elastic solids. The first approach is based on the theory of selfadjoint extensions of differential operators. In the second approach function spaces with separated asymptotics and point asymptotic conditions are introduced, and a variational formulation is established. For both approaches, accuracy estimates are derived.
Localization effects for eigenfunctions near to the edge of a thin domain
Topological derivatives for semilinear elliptic equations
The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L∞ norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.
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