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On time-harmonic Maxwell equations with nonhomogeneous conductivities: Solvability and FE-approximation

Michal KřížekPekka Neittaanmäki — 1989

Aplikace matematiky

The solvability of time-harmonic Maxwell equations in the 3D-case with nonhomogeneous conductivities is considered by adapting Sobolev space technique and variational formulation of the problem in question. Moreover, a finite element approximation is presented in the 3D-case together with an error estimate in the energy norm. Some remarks are given to the 2D-problem arising from geophysics.

Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains

Michal KřížekPekka Neittaanmäki — 1984

Aplikace matematiky

The authors examine a finite element method for the numerical approximation of the solution to a div-rot system with mixed boundary conditions in bounded plane domains with piecewise smooth boundary. The solvability of the system both in an infinite and finite dimensional formulation is proved. Piecewise linear element fields with pointwise boundary conditions are used and their approximation properties are studied. Numerical examples indicating the accuracy of the method are given.

Shape optimization in contact problems based on penalization of the state inequality

Jaroslav HaslingerPekka NeittaanmäkiTimo Tiihonen — 1986

Aplikace matematiky

The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established.

On FE-grid relocation in solving unilateral boundary value problems by FEM

Jaroslav HaslingerPekka NeittaanmäkiKimmo Salmenjoki — 1992

Applications of Mathematics

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...

Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type

Liping LiuMichal KřížekPekka Neittaanmäki — 1996

Applications of Mathematics

A nonlinear elliptic partial differential equation with homogeneous Dirichlet boundary conditions is examined. The problem describes for instance a stationary heat conduction in nonlinear inhomogeneous and anisotropic media. For finite elements of degree k 1 we prove the optimal rates of convergence 𝒪 ( h k ) in the H 1 -norm and 𝒪 ( h k + 1 ) in the L 2 -norm provided the true solution is sufficiently smooth. Considerations are restricted to domains with polyhedral boundaries. Numerical integration is not taken into account....

Second-order optimality conditions for nondominated solutions of multiobjective programming with C 1 , 1 data

Liping LiuPekka NeittaanmäkiMichal Křížek — 2000

Applications of Mathematics

We examine new second-order necessary conditions and sufficient conditions which characterize nondominated solutions of a generalized constrained multiobjective programming problem. The vector-valued criterion function as well as constraint functions are supposed to be from the class C 1 , 1 . Second-order optimality conditions for local Pareto solutions are derived as a special case.

Galerkin approximations for the linear parabolic equation with the third boundary condition

István FaragóSergey KorotovPekka Neittaanmäki — 2003

Applications of Mathematics

We solve a linear parabolic equation in d , d 1 , with the third nonhomogeneous boundary condition using the finite element method for discretization in space, and the θ -method for discretization in time. The convergence of both, the semidiscrete approximations and the fully discretized ones, is analysed. The proofs are based on a generalization of the idea of the elliptic projection. The rate of convergence is derived also for variable time step-sizes.

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