Polynomial extensions play a vital role in analysis of the p and h-p FEM as well as spectral element method. In this paper, we construct explicitly polynomial extensions on a triangle T and a square S, which lift a polynomial defined on a side Γ or on whole boundary of T or S. The continuity of these extension operators from H 1 2 00(Γ) to H (T ) or H(S) and from H 1 2 (∂T ) to H(T ) or from H ...

In this paper we show that we can use a modified version of the h-p spectral element method proposed in [6,7,13,14] to solve elliptic problems with general boundary conditions to exponential accuracy on polygonal domains using nonconform-ing spectral element functions. A geometrical mesh is used in a neighbourhood of the corners. With this mesh we seek a solution which minimizes the sum of a we...

Detecting damages in its early stage, and hence, to ensure the safety and reliability of structures is of vital important. Guided waves have been recognised as one of the promising damage detection techniques that are sensitive to small and different types of damages. The understanding of guided wave propagation and scattering phenomena at the damages is one of the fundamental elements to facil...

Certain results of numerical simulations obtained by the use of the spectral finite element method in time domain are presented by the authors. They were selected in order to show the effectiveness of the spectral finite element method for investigation of problems associated with propagation of guided elastic waves in a wind turbine laminated composite blade. Results of these simulations were ...

A least-squares spectral finite element method was used to develop an accurate computer code for prediction of solidification from a melt under the influence of an externally applied magnetic field. The computational results indicate significantly different flow-field patterns and thermal fields in the melt and the accrued solid in the cases of full gravity, reduced gravity, and an applied unif...

We examine the dual graph representation of simplicial manifolds in causal dynamical triangulations (CDT) as a means to build observables and propose new based on finite element methods (FEM). In particular, with application FEM techniques, we extract (low-lying) spectrum Laplace-Beltrami (LB) operator Sobolev space ${H}^{1}$ scalar functions piecewise flat compare them corresponding results ob...

Leakage reactance is one of the most important specifications in transformer that has significant impact on its overall design. Variation in leakage reactance serves as a diagnostic measure to indicate mechanical integrity of power transformers before and after a short circuit test that demonstrates mechanical strength of transformer windings. This paper presents an approach for leakage reactan...

Power transformers represent the largest portion of capital investment in transmission and distribution substations. In addition, power transformer outages have a considerable economic impact on the operation of an electrical network. One of the most important parameters’ governing a transformer’s life expectancy is the hot-spot temperature value. Due to under estimation of stray losses in powe...

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...

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...