Extensions of Variational Methods, II

Variational Methods and Periodic Solutions of Kirchhoff-type Equations. Ii

In a previous paper [1], the author and Shmel’tser started the construction of an extended Lyusternik–Shnirelman–Morse theory for the study of single-valued and multivalued functionals on the space Ω̂(M) of losed directed curves in a manifold M. The authors applied these methods to the classical problem (Kirchhoffs problem) about the free motion of a rigid body in an ideal incompressible liquid,...

Monotone Multigrid Methods for Elliptic Variational Inequalities Ii 1

We derive fast solvers for discrete elliptic variational inequalities of the second kind as resulting from the approximation by piecewise linear nite elements. Following the rst part of this paper, monotone multigrid methods are considered as extended underrelaxations. Again, the coarse grid corrections are localized by suitable constraints, which in this case are xed by ne grid smoothing. We c...

Monotone Multigrid Methods for Elliptic Variational Inequalities Ii

We derive fast solvers for discrete elliptic variational inequalities of the second kind as resulting from the approximation by piecewise linear nite elements. Following the rst part of this paper, monotone multigrid methods are considered as extended underrelaxations. Again, the coarse grid corrections are localized by suitable constraints, which in this case are xed by ne grid smoothing. We c...

A Survey of Direct Methods for Solving Variational Problems

This study presents a comparative survey of direct methods for solving Variational Problems. Thisproblems can be used to solve various differential equations in physics and chemistry like RateEquation for a chemical reaction. There are procedures that any type of a differential equation isconvertible to a variational problem. Therefore finding the solution of a differential equation isequivalen...

Variational Formulation of Problems and Variational Methods