On the Construction of Lusternik-Schnirelmann Critical Values with Application to Bifurcation Problems

An iterative method to construct Lusternik-Schnirelmann critical values is presented. Examples of its use to obtain numerical solutions to nonlinear eigenvalue problems and their bifurcation branches are given. peerReviewed

Innovatiivinen tutkimusympäristö innostaa : Pääkirjoitus

Agora muodostaa kohtaamispaikan, jossa yrityselämä, yhteiskunta ja yliopisto voivat yhdessä ponistella kehittääkseen uusia teknologisia ja sosiaalisia innovaatioita.

Solvability of a first order system in three-dimensional non-smooth domains

summary:A system of first order partial differential equations is studied which is defined by the divergence and rotation operators in a bounded nonsmooth domain $\Omega\subset \bold R^3$. On the boundary $\delta\Omega$, the vanishing normal component is prescribed. A variational formulation is given and its solvability is investigated.

Computational mechanics in Finland

On the validity of Friedrichs’ inequalities

A standard proof of Friedrich's second inequality is based on contradiction argumentation. In this paper a direct proof is presented. Moreover, necessary and sufficient conditions for the validity of Friedrichs' first and second inequality are given for plane domains. peerReviewed

A Theory of electrical circuits with resistively coupled distributed structures : Delay time predicting

This paper deals with qualitative properties ( existence, uniqueness, and especially, stability) and numerical solution of a circuit consisting of a resistive multiport with r-c-g "exactly modeled" distributed elements connected to its terminals. This kind of results are useful, for instance, when we study the effect of interconnections on the speed of transient process from an integrated structure. A formula to evaluate the delay time as a global parameter of the circuit is given and verified by numerical calculus. peerReviewed

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

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 probJem 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. peerReviewed

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

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. peerReviewed

A neural approach of dynamic priority assignment in a queueing network

Regularization and finite element approximation of the wave equation with Dirichlet boundary data

A numerical method for solving the wave equation with nonhomogenuous, nonsmooth Dirichlet boundary condition is proposed. Convergence of the method is proved and some erràr estimates are derived [L-S-2]. The method is based on the regularization technique [L-1], [L-S-l] of the wave equation with Dirichlet bounàary data. Several numerical results are provided in two dimensional case. peerReviewed