The performance of finite element computation depends strongly on the quality of the geometric mesh and the efficiency of the numerical solution of the linear systems resulting from the discretization of partial differential equation (PDE) models. It is common knowledge that mesh geometry affects not only the approximation error of the finite element solution but also the spectral properties of...

A spectral element library has been developed and integrated with the M3D extended MHD code. The currently used linear triangular finite element implementation and the new high order quadrilateral spectral element implementation are directly compared on equilibrium, linear stability, and nonlinear evolution calculations run on the same problems. AMS subject classifications: 65M70 PACS: 52.65.Kj

In the past few years we have been involved in the development and implementation of parallel finite element and pseudo-spectral methods for porous media flow. In this paper we present a brief review of our methods and show several examples of highly nonlinear simulations in two and three-dimensions, on different current high performance computers. New issues on finite element techniques and ps...

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 ...

If the nodes for the spectral element method are chosen to be the Gauss-LegendreLobatto points, then the resulting mass matrix is diagonal and the method is sometimes then described as the Gauss-point mass lumped finite element scheme. We study the dispersive behaviour of the scheme issue in detail and provide both a qualitative description of the nature of the dispersive and dissipative behavi...

The spectral element method (SEM) is a high order numerical method for solving partial differential equations that inherits the accuracy of spectral methods and the geometrical flexibility of the finite element method. These lectures provide an introduction to the SEM for graduate students in Earth science. The construction of the method is described for a model problem in 1D and 2D. The elemen...