In this paper, structure-preserving time-integrators for rigid body-type mechanical systems are derived from a discrete Hamilton–Pontryagin variational principle. From this principle, one can derive a novel class of variational partitioned Runge– Kutta methods on Lie groups. Included among these integrators are generalizations of symplectic Euler and Störmer–Verlet integrators from flat spaces ...

We combine a dual-mixed finite element method with a Dirichletto-Neumann mapping (derived by the boundary integral equation method) to study the solvability and Galerkin approximations of a class of exterior nonlinear transmission problems in the plane. As a model problem, we consider a nonlinear elliptic equation in divergence form coupled with the Laplace equation in an unbounded region of th...

This paper is concerned with the existence of two non-trivial weak solutions for a p(x)-Kirchho type problem by using the mountain pass theorem of Ambrosetti and Rabinowitz and Ekeland's variational principle and the theory of the variable exponent Sobolev spaces.

In this paper we revive a special, less-common, variational principle in analytical mechanics (Hertz’ of least curvature) to develop novel analogue Euler's equations for the dynamics an ideal fluid. The new formulation is fundamentally different from those formulations based on Hamilton's action. Using formulation, generalize century-old problem flow over two-dimensional body; developed closure...