This paper introduces a new method for the development of closed-form spatial Green’s functions for electrostatic problems involving layered dielectrics. The new method utilizes a finite-difference approximation of the spectral domain form of the Green’s function to overcome the tedious numerical integration of the Fourier–Bessel inverse transform that is required to generate the Green’s functi...

The numerical integration of partial differential equations is a particularly difficult task, and there is no generally applicable method. In contrast to ordinary differential equations, the most natural explicit finite difference methods such as replacing differentials by forward, backward, or central finite differences often are numerically unstable, even in the limit of very small discretiza...

There are different finite element models in place for predicting the bending behavior of shear deformable beams and plates. Mostly, the literature abounds with traditional equi-spaced Langrange based low order finite element approximations using displacement formulations. However, the finite element models of Timoshenko beams and Mindlin plates with linear interpolation of all generalized disp...

We discuss a priori error estimates for a semidiscrete piecewise linear finite volume element (FVE) approximation to a second order wave equation in a two-dimensional convex polygonal domain. Since the domain is convex polygonal, a special attention has been paid to the limited regularity of the exact solution. Optimal error estimates in L2, H1 norms and quasioptimal estimates in L∞ norm are di...

In this article, we discuss the numerical approximation of transport phenomena occurring at material interfaces between physical subdomains with heterogenous properties. The model in each subdomain consists of a partial differential equation with diffusive, convective and reactive terms, the coupling between each subdomain being realized through an interface transmission condition of Robin type...

This paper presents a physical approach to simulate objects deformation in images. To physically model the given objects the finite element method is used, and to match the objects’ nodes modal analysis is considered. The desired displacement field is estimated through the dynamic equilibrium equation. To solve this differential equation different integration methods can be used. In this paper ...

Summation-by-parts (SBP) finite-difference discretizations share many attractive properties with Galerkin finite-element methods (FEMs), including time stability and superconvergent functionals; however, unlike FEMs, SBP operators are not completely determined by a basis, so the potential exists to tailor SBP operators to meet different objectives. To date, application of highorder SBP discreti...

The periodic initial value problem for the partial differential equation ut + uxxx + ß(u )x + 2{u )xx + euxx ôutx = 0, e , ô > 0, arises in fluidization models. The numerical integration of the problem is a difficult task in that many "reasonable" finite difference and finite element methods give rise to unstable discretizations. We show how to modify the standard Galerkin technique in order to...

Several stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are numerically investigated. They are penalty, regular, multiscale enrichment, and local Gauss integration method. Comparisons between them are carried out, which show that the local Gauss integration method has good stability, efficiency, and accuracy properties, and...

in this paper, the propagation of the waves in the laminated composite plates which is subjected to low velocity impact is investigated using the finite element method. a rigid metallic projectile with spherical nose is considered and the impact of this projectile with laminated composite is studied in this study. considering a finite element model the governing equations of the problem is disc...