Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, tota...

In this study, acoustic wave scattering in a homogeneous media by an obstacle is examined the case of plane excitation and formation jets explored. Spectral element method (SEM) employed for approximate solution scattered waves’ calculations. An important finding study concurrence whispering gallery modes jet proper adjustment structural parameters, which has not been reported before literature...

A nonconforming spectral element method for the Stokes problem on nonsmooth domains has been proposed in Mohapatra et al. (J Comput Appl Math 372:112696, 2020). The main focus of this article is to study performance problems smooth curvilinear and with mixed boundary conditions. Various test cases are considered including generalized $${\mathbb {R}}^{2}$$ {R}}^{3}$$ verify exponential accuracy ...

Abstract The Spectral Finite Element Technique (SFEM) has Several Applications in the Sciences, Engineering, and Mathematics, which will be Covered this Review Article. Method is a Variant of Traditional FEM that Makes use Higher Order Basis Functions (FEM). One most Fundamental Numerical Techniques Employed Simulation SFEM, Outperforms Other Terms Faster Convergence, Reduced Diffusion Dispersi...

The Lagrange-Galerkin spectral element method for the two-dimensional shallow water equations is presented. The equations are written in conservation form and the domains are discretized using quadrilateral elements. Lagrangian methods integrate the governing equations along the characteristic curves, thus being well suited for resolving the nonlinearities introduced by the advection operator o...