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Displaying 121 –
140 of
268
In this paper we present theoretical, computational, and practical aspects concerning 3-dimensional shape optimization governed by linear magnetostatics. The state solution is approximated by the finite element method using Nédélec elements on tetrahedra. Concerning optimization, the shape controls the interface between the air and the ferromagnetic parts while the whole domain is fixed. We prove the existence of an optimal shape. Then we state a finite element approximation to the optimization...
Error estimates for the mixed finite element solution of
4th order elliptic problems with variable coefficients, which,
in the particular case of aniso-/ortho-/isotropic plate bending problems,
gives a direct, simultaneous approximation to bending moment tensor
field and displacement field
'u', have been developed considering the combined effect of
boundary approximation and numerical integration.
We consider an elliptic pseudodifferential equation in a multi-dimensional cone, and using the wave factorization concept for an elliptic symbol we describe a general solution of such equation in Sobolev-Slobodetskii spaces. This general solution depends on some arbitrary functions, their quantity being determined by an index of the wave factorization. For identifying these arbitrary functions one needs some additional conditions, for example, boundary conditions. Simple boundary value problems,...
We investigate the existence and stability of solutions for higher-order two-point boundary value problems in case the differential operator is not necessarily positive definite, i.e. with superlinear nonlinearities. We write an abstract realization of the Dirichlet problem and provide abstract existence and stability results which are further applied to concrete problems.
We consider singular perturbation variational problems depending on a small parameter . The right hand side is such that the energy does not remain bounded as . The asymptotic behavior involves internal layers where most of the energy concentrates. Three examples are addressed, with limits elliptic, parabolic and hyperbolic respectively, whereas the problems with are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after integrating...
We consider singular perturbation variational problems
depending on a small parameter ε. The right hand side is such
that the energy
does not remain bounded as ε → 0. The asymptotic
behavior involves internal
layers where most of the energy concentrates. Three examples are addressed,
with limits elliptic, parabolic and hyperbolic respectively, whereas the
problems with ε > 0 are elliptic. In the parabolic and hyperbolic
cases, the
propagation of singularities appear as an integral property after...
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268