In this paper, the spectral element (SE) method is applied in time to find the entire time-periodic or transient solution of time-dependent differential equations. The time-periodic solution is computed by enforcing periodicity of the element set. Of particular interest are periodic forcing functions possessing high frequency content. To maintain the spectral accuracy for such forcing functions...

a non-linear finite element model could be a useful tool in the development of a method of predicting soil pressure-sinkage behaviour, and can be used to investigate and analyze soil compaction. this study was undertaken to emphasize that the finite element method (fem) is a proper technique to model soil pressure-sinkage behaviour. for this purpose, the finite element method was used to model ...

The non-hydrostatic (NH) compressible Euler equations of dry atmosphere are solved in a simplified two dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. The SEM uses high-order nodal basis functions asso-5 ciated with Lagrange polynomials based on Gauss–Lobatto–Legen...

Computational physics has become an essential research and interpretation tool in many fields. Particularly, in reservoir geophysics, ultrasonic and seismic modeling in porous media is used to study the properties of rocks and characterize the seismic response of geological formations. Here, we give a brief overview of the most common numerical methods used to solve the partial differential equ...

We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions, the latter...