In this paper, we introduce and analyze a special mortar finite element method. We restrict ourselves to the case of two disjoint subdomains, and use RaviartThomas finite elements in one subdomain and conforming finite elements in the other. In particular, this might be interesting for the coupling of different models and materials. Because of the different role of Dirichlet and Neumann boundar...

We summarise research reported in (Efroimsky 2002, 2003; Efroimsky & Goldreich 2003a,b) and develop its application to planetary equations in non-inertial frames. Whenever a standard system of six planetary equations (in the Lagrange, Delaunay, or other form) is employed, the trajectory resides on a 9(N-1)-dimensional submanifold of the 12(N-1)-dimensional space spanned by the orbital elements ...

The solution of themulti-dimensional Schrödinger equation in the generalized spherical coordinates is constructed in the Lagrange-meshmethod. Laguerre and Jacobimeshes are used to constructmatrix elements for the generalizedHamiltonian. Thematrix elements are functions of quadrature abscissas and involve few free parameters for each angular dimension. A ring-shaped non-central separable potenti...

In 2004, Bajard, Imbert and Plantard introduced a new system of representation to perform arithmetic modulo a prime integer p, the Adapted Modular Number System (AMNS). In this system, the elements are seen as polynomial of degree n − 1 with the coefficients of size p. The best method for multiplication in AMNS works only for some specific moduli p. In this paper, we propose a novel algorithm t...

Based on Lagrange and Hermite interpolation two novel versions of weak form quadrature element are proposed for a non-classical Euler-Bernoulli beam theory. By extending these concept two new plate elements are formulated using Lagrange-Lagrange and mixed Lagrange-Hermite interpolations for a non-classical Kirchhoff plate theory. The non-classical theories are governed by sixth order partial di...

Reduced order models employing the Lagrange and POD reduced basis methods in numerical approximation and feedback control of systems are presented and numerically tested. The system under consideration is a thin cylindrical shell with surface-mounted piezoceramic actua-tors. Donnell-Mushtari equations, modiied to include Kelvin-Voigt damping, are used to model the system dynamics. Basis functio...

In the present paper, some finite element softwares about interaction of dam and reservoir during earthquake in time domain are discussed. Impedance option is used as boundary condition of absorbent of reservoir and wave. For each software, time history analysis of pressure and displacement are done and finally suitable elements for dam structure and reservoir fluid are introduced comparing the...