Vol 37, No 5 (2016)

In this paper a new functional a posteriori error estimate is obtained for problems of bending of curvilinear Timoshenko beams. For sake of simplicity clamped beams under the action of traverse and axial forces and bending moment are considered. The derived estimate is reliable, is applicable to any conforming approximation and can be used both for global accuracy control and for local error indication for subsequent mesh adaptation. Its theoretical properties are confirmed by results of numerical experiments.

In this paper we derive the monotonicity conditions for condensed-algebraic systems obtained by the discretization of the Poisson’s problem by the classical lowest order Raviart–Thomas (RT₀) and the piece-wise constant fluxes (PWCF) MFE methods on triangular and tetrahedral meshes. We also establish the correspondence between the condensed system matrices resulting from application of these two methods.

The discrete maximum principle is a meaningful requirement for numerical schemes used in multiphase flow models. It eliminates numerical pressure overshoots and undershoots, which may cause unnatural Darcy velocities and wrong numerical saturations. In this paper we study the application of the nonlinear finite volume method with discrete maximum principle [1] to the two-phase flow model. The method satisfies the discrete maximum principle for numerical pressures of incompressible fluids with neglected capillary pressure. For non-zero capillary pressure and constant phase viscosities the discrete maximum principle holds for numerical global pressure.

The nonlinear eigenvalue problem describing eigenvibrations of a beam with elastically attached load is investigated. The existence of an increasing sequence of positive simple eigenvalues with limit point at infinity is established. To the sequence of eigenvalues, there corresponds a system of normalized eigenfunctions. The problem is approximated by the finite element method with Hermite finite elements of arbitrary order. The convergence and accuracy of approximate eigenvalues and eigenfunctions are investigated.

We propose a new two-level iterative method for solution of a general problem of optimal allocation of a homogeneous resource (bandwidth) in a wireless communication network. It is divided into service zones (clusters) and the network manager can buy external volumes of this resource. This approach leads to a convex optimization problem, which is solved with a dual Lagrangian method, where calculation of the cost function value decomposes into a system of independent zonal optimization problems. Each of them is treated as a market equilibrium problem. This optimization problem is solved with conditional gradient method for different information exchange schemes for participants. Besides, we suggest several ways to adjust the basic problemto the case of moving nodes. We give some results of numerical experiments on the proposed method which confirm its preference over the previous ones.