When derivatives of a spectral element solution are used in a different context, such as visualization or in calculations with a different numerical method, the discontinuity of the derivatives at the element interfaces is a potential problem. Asymptotically, the jumps in the derivatives decay spectrally fast, but it is not always possible or efficient use of computational resources to repeat t...

An eXtended Stochastic Finite Element Method has been recently proposed for the numerical solution of partial di erential equations de ned on random domains. This method is based on a mariage between the eXtended Finite Element Method and spectral stochastic methods. In this paper, we propose an extension of this method for the numerical simulation of random multi-phased materials. The random g...

in this paper, the dierential transform method (dtm) is applied to the fisherequation. this method can be used to obtain the exact solutions of fisherequation. finally, we give some examples to illustrate the suciency of themethod for solving such nonlinear partial dierential equations. these resultsshow that this technique is easy to apply.

Fluid motion driven by planetary libration may play a key role in maintaining the magnetism of synchronous planets and moons that are thermally or chemically non-convective. We present a fully discrete finite element method on a triaxial ellipsoidal domain for simulating a three-dimensional nonlinear flow in a latitudinally librating triaxial ellipsoidal cavity, for which the usual pseudo-spect...

Block Krylov subspace spectral (KSS) methods are a “best-of-both-worlds” compromise between explicit and implicit time-stepping methods for variable-coefficient PDE, in that they combine the efficiency of explicit methods and the stability of implicit methods, while also achieving spectral accuracy in space and high-order accuracy in time. Block KSS methods compute each Fourier coefficient of t...

A spectral element formulation of the atmospheric two-dimensional shallow water equations on the cubed-sphere is described. The equations are written in tensor form using the contravariant and covariant velocity components. A semi-implicit time discretization results in a reduced Schur complement system for the pressure. The Laplacian operator is approximated by the L2 pseudo-Laplacian arising ...

The implementation of high-order (spectral) approximations associated with FEM is an approach to overcome the difficulties encountered in the numerical analysis of complex problems. This paper proposes the use of the spectral finite element method, originally developed for computational fluid dynamics problems, to achieve improved solutions for these types of problems. Here, the interpolation n...