Eliseo Chacón Vera

Numerical calculations of two-dimensional EHD plumes with finite element and particle methods

A numerical technique mixing finite element and particle methods is used to study numerically EHD two-dimensional plumes. The results of three calculations for different injection strengths are shown. A brief discussion of these results follows.

A three field stabilized finite element method for the Stokes equations

Abstract We consider in this work the boundary value problem for Stokes equations on a two dimensional domain in cases where non-standard boundary conditions are given. We study the cases where pressure and normal or tangential components of the velocity are given in different parts of the boundary and solve the problem with a minimal regularity. We introduce the problem and its variational formulation which is a mixed one. The principal unknowns are the pressure and the vorticity, the multiplier is the velocity. We present the numerical discretization which needs some stabilization. We prove the convergence and the behavior of the a priori error estimates. Some numerical tests are also presented. To cite this article: M. Amara et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 603–608.

A non-overlapping domain decomposition method for the Stokes equations via a penalty term on the interface

Abstract The purpose of this Note is to perform a theoretical analysis of the domain decomposition method introduced in [2]. We motivate and introduce an improvement of this method and carry out the analysis when it is applied to solving the Stokes equations. Our method is based on a penalty term on the interface between subdomains that enforces the appropriate transmission conditions and may be seen as variation of the Robin method. We obtain strong convergence results for velocity and pressure in the standard H 1 and L 2 norms and precise rates of convergence, together with error estimates. These error estimates are of optimal order with respect to the precision of the interpolation. We conclude with some numerical tests. To cite this article: T. Chacon Rebollo, E. Chacon Vera, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 221–226.

A non-standard FETI-DP mortar method for Stokes problem

Abstract - The trace spaces H1/2 and H1/2 00 play a key role in the FETI and mortar families of domain decomposition methods. However, a direct numerical evaluation of these norms is usually avoided. On the other hand, and for stability issues, the subspace of functions for which their jumps across the interfaces of neighbouring subdomains belong to these trace spaces yields a more suitable framework than the standard broken Sobolev space. Finally, the nullity of these jumps is usually imposed via Lagrange multipliers and using the pairing of the trace spaces with their duals. A direct computation of these pairings can be performed using the Riesz-canonical isometry. In this work we consider all these ingredients and introduce a domain decomposition method that falls into the FETI-DP mortar family. The application is to the incompressible Stokes problem and we see that continuous bounds are replicated at the discrete level. As a consequence, no stabilization is required. Some numerical tests are finally presented.