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- E Ahusborde, R Gruber, M Azaiez, M L Sawley
- Physical review. E, Statistical, nonlinear, and…
- 2007

A general high-order finite element method for solving partial differential equations, called the COnstraints Oriented Library (COOL) method, is presented. This hp approach takes into account the underlying nature of the corresponding physical problem, and thus avoids the generation of nonphysical solutions. In the COOL method, all terms in a variational… (More)

- Etienne Ahusborde
- Numerical Algorithms
- 2008

This paper extends previous studies of the application of Legendre spectral methods to the grad (div) eigenvalue problem on a quadrangular domain in $I\!\!R^2$ . The extension focuses on natural boundary conditions. Spectral approximations based on primal and dual variational approaches are built using Gaussian quadrature rules both on single (i.e.… (More)

- Etienne Ahusborde, Mejdi Azaïez, Jean-Paul Caltagirone
- J. Comput. Physics
- 2007

In 1999, Jean-Paul Caltagirone and Jérôme Breil have developed in their paper [Caltagirone, J. Breil, Sur une méthode de projection vectorielle pour la résolution des équations de Navier–Stokes, C.R. Acad. Sci. Paris 327(Série II b) (1999) 1179–1184] a new method to compute a divergence-free velocity. They have used the grad(div) operator to extract the… (More)

- Etienne Ahusborde, Mustapha El Ossmani
- Mathematics and Computers in Simulation
- 2017

- Etienne Ahusborde, Mejdi Azaïez, Faker Ben Belgacem, E. Palomo Del Barrio
- J. Comput. Physics
- 2015

- E. Ahusborde, M. Azaı̈ez, M. O. Deville, E. H. Mund
- 2008

This paper describes an iterative solution technique for partial differential equations involving the grad(div) operator, based on a domain decomposition. Iterations are performed to solve the solution on the interface. We identify the transmission relationships through the interface. We relate the approach to a Steklov-Poincaré operator, and we illustrate… (More)

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