This paper is about discrete sensitivity analysis. A triangular bending element with constant moment and six degrees of freedom is used. The required derivatives for sensitivity analysis are calculated explicitly. These formulations, finite element method and sequential linear programming are utilized to find shape optimization of plate bending structures. The numerical examples, which show the...

We introduce a new class of higher order mixed finite volume methods for elliptic problems. We start from the usual way of changing the given equation into a mixed system using the Darcy’s law, u = −K∇p. By integrating the system of equations with some judiciously chosen test spaces on each element, we define new mixed finite volume methods of higher order. We show that these new schemes are eq...

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

In the present study, a spectral finite element method is developed for free and forced transverse vibration of Levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. Levy solution assumption was used to convert the two-dimensional problem into a one-dimensional problem. In the first step, the governing out-of-plane differential equations are tr...

An adaptive mixed finite element method (AMFEM) is designed to guarantee an error reduction, also known as saturation property: after each refinement step, the error for the fine mesh is strictly smaller than the error for the coarse mesh up to oscillation terms. This error reduction property is established here for the Raviart–Thomas finite element method with a reduction factor ρ < 1 uniforml...

We construct a new family of semi-discrete numerical schemes for the approximation of the one-dimensional periodic Vlasov-Poisson system. The methods are based on the coupling of discontinuous Galerkin approximation to the Vlasov equation and several finite element (conforming, non-conforming and mixed) approximations for the Poisson problem. We show optimal error estimates for the all proposed...

In this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $Z_{2}$. We also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

This paper deals with applications of the “Discrete-Duality Finite Volume” approach to a variety of elliptic problems. This is a new finite volume method, based on the derivation of discrete operators obeying a Discrete-Duality principle. An appropriate choice of the degrees of freedom allows one to use arbitrary meshes. We show that the method is naturally related to finite and mixed finite el...

Three-dimensional enriched finite elements are used to compute mixed-mode stress intensity factors (SIFs) for three-dimensional cracks in elastic functionally graded materials (FGMs) that are subject to general mixed-mode loading. The method, which advantageously does not require special mesh configuration/modifications and post-processing of finite element results, is an enhancement of previou...