Neumann problem in a class of harmonic functions in domains with a piecewise-Lyapunov boundary.
Nonhomogeneous boundary conditions and curved triangular finite elements
Approximation of nonhomogeneous boundary conditions of Dirichlet and Neumann types is suggested in solving boundary value problems of elliptic equations by the finite element method. Curved triangular elements are considered. In the first part of the paper the convergence of the finite element method is analyzed in the case of nonhomogeneous Dirichlet problem for elliptic equations of order , in the second part of the paper in the case of nonhomogeneous mixed boundary value problem for second order...
Non-trivial solutions for a class of (p₁,...,pₙ)-biharmonic systems with Navier boundary conditions
Using a recent critical point theorem due to Bonanno, the existence of a non-trivial solution for a class of systems of n fourth-order partial differential equations with Navier boundary conditions is established.
Normal solvability of general linear elliptic problems.
Numerical analysis of the general biharmonic problem by the finite element method
The present paper deals with solving the general biharmonic problem by the finite element method using curved triangular finit -elements introduced by Ženíšek. The effect of numerical integration is analysed in the case of mixed boundary conditions and sufficient conditions for the uniform -ellipticity are found.