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...

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...

Climate modeling encompasses an enormous range of spatial and temporal scales. One of its great remaining challenges is bridging the scale gaps between global climate processes, basinscale and regional impacts, and smaller-scale ecosystem dynamics. Improving and accessing enhanced computational resources will help bridge this gap. Nonetheless, enhanced computer power alone is insufficient witho...

We study the ability of high order numerical methods to propagate discrete waves at the same speed as the physical waves in the case of the one-way wave equation. A detailed analysis of the finite element method is presented including an explicit form for the discrete dispersion relation and a complete characterisation of the numerical Bloch waves admitted by the scheme. A comparision is made w...

A parallel element-by-element ,nultilevel strategy is developed and applied to two nonlinear, coupled PDE system.•. Spectral (p) finite elements are used to discretize the lems and the multilevel solution strategy uses projections between bases of different degree (level). The projection methods for the p-multilevel schemes are developed and analyzed for Lagrange and hierarchic bases. The appro...

We study the dispersion and dissipation of the numerical scheme obtained by taking a weighted averaging of the consistent (finite element) mass matrix and lumped (spectral element) mass matrix for the small wavenumber limit. We find and prove that for the optimum blending the resulting scheme (a) provides 2p+4 order accuracy for p-th order method (two orders more accurate compared with finite a...

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...