All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as expressly permitted by law, without either the prior written permission of the Publisher, or authorization through payment of the appropriate photocopy fee to the Copyright ...

Our work concerns the approximation of the 2D Stokes equations solution based on a variational formulation with primitive variables: velocity and pressure. We choose to use the mortar spectral element method which is a domain decomposition technique. Since, this method has a high spatial and temporal complexity, we opted to parallel processing. We present, in this paper, two versions of sequent...

Spectral element approximations based on triangular elements and on the so-called Fekete points of the triangle have been recently developed. p-multigrid methods offer an interesting way to resolve efficiently the resulting ill-conditioned algebraic systems. For elliptic problems, it is shown that a well chosen restriction operator and a good set up of the coarse grid matrices may lead to valua...

From a mathematical point of view the fundamental challenge of computational fluid dynamics arises from nonlinear terms in the governing dynamical equations, of which the prototype is the flow velocity ~u and its advection (~u· ~ ∇)~u. It is commonly known that the most accurate and efficient method to compute the gradient (~ ∇) part is the spectral method, in which ~u(~x) is approximated at ea...

This paper presents an analytical method to compute the leakage inductances of power transformers with a turn-to-turn winding fault. A leakage inductance model to represent the transformer with faulty turns is also proposed. The results obtained from the application of the analytical method are validated by using data obtained from finite-element analysis and experimental tests.

The solution of elliptic boundary value problems often leads to singularities due to nonsmoothness of the domains on which the problem is posed. This paper studies the performance of the nonconforming hp/spectral element method for elliptic problems on non smooth domains. This paper deals with monotone singularities of type rα and rα log r as well as the oscillating singularities of type rα sin...

We consider the viscous Burgers equation with a fractional nonlinear term as a model involving non-local nonlinearities in conservation laws, which, surprisingly, has an analytical solution obtained by a fractional extension of the Hopf-Cole transformation. We use this model and its inviscid limit to develop stable spectral and discontinuous Galerkin spectral element methods by employing the co...