Hyam Abboud

Hyam Abboud
Lebanese University · Faculty of Science

PhD

About

13
Publications
2,066
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115
Citations
Introduction
Hyam Abboud currently works at the department of mathematics at the faculty of sciences II of the Lebanese University. Hyam does research in Mathematical Analysis and Applied Mathematics.

Publications

Publications (13)
Article
Full-text available
We introduce a family of bi-grid schemes in finite elements for solving 2D incompressible Navier-Stokes equations in velocity and pressure (u; p). The new schemes are based on projection methods and use two pairs of FEM spaces, a sparse and a fine one. The main computational e ortis done on the coarsest velocity space with an implicit and unconditi...
Preprint
Full-text available
We introduce a family of bi-grid schemes in finite elements for solving 2D incompressible Navier-Stokes equations in velocity and pressure $(u,p)$. The new schemes are based on projection methods and use two pairs of FEM spaces, a sparse and a fine one. The main computational effort is done on the coarsest velocity space with an implicit and uncond...
Article
Full-text available
In this work, we propose a bi-grid scheme framework for the Allen-Cahn equation in Finite Element Method. The new methods are based on the use of two FEM spaces, a coarse one and a fine one, and on a decomposition of the solution into mean and fluctuant parts. This separation of the scales, in both space and frequency, allows to build a stabilizati...
Preprint
In this work, we propose a bi-grid scheme framework for the Allen-Cahn equation in Finite Element Method. The new methods are based on the use of two FEM spaces, a coarse one and a fine one, and on a decomposition of the solution into mean and fluctuant parts. This separation of the scales, in both space and frequency, allows to build a stabilizati...
Article
Full-text available
In this article, we study the Stokes problem with some nonstandard boundary conditions. The variational formulation decouples into a system for the velocity and a Poisson equation for the pressure. The corresponding discrete system do not need an inf-sup condition. Hence, the velocity is approximated with “curl” conforming finite elements and the p...
Article
Full-text available
This work is devoted to the optimal and a posteriori error estimates of the Stokes problem with some non-standard boundary conditions in three dimensions. The variational formulation is decoupled into a system for the velocity and a Poisson equation for the pressure. The velocity is approximated with curl conforming finite elements and the pressure...
Article
Full-text available
We study a second-order two-grid scheme fully discrete in time and space for solving the Navier–Stokes equations. The two-grid strategy consists in discretizing, in the first step, the fully non-linear problem, in space on a coarse grid with mesh-size H and time step Δt and, in the second step, in discretizing the linearized problem around the velo...
Article
Full-text available
In this paper, we propose a finite-element scheme for solving numerically the equations of a transient two-dimensional grade-two non-Newtonian Rivlin–Ericksen fluid model. This system of equations is considered an appropriate model for the motion of a water solution of polymers. By introducing a new variable denoted z, we split the problem into a c...
Article
Full-text available
We study a two-grid scheme fully discrete in time and space for solving the Navier-Stokes system. In the first step, the fully non-linear problem is discretized in space on a coarse grid with mesh-size H and time step k. In the second step, the problem is discretized in space on a fine grid with mesh-size h and the same time step, and linearized arou...
Article
Full-text available
We develop a numerical method for solving Maxwell's equations on a grid involving zones with cells of very different sizes, in order for example to compute sources coming from particles which need to be resolved on a very fine grid. The method is based on domain decomposition techniques which lead us to introduce two auxiliary problems and show the...
Article
Full-text available
This thesis focuses on the time-dependent incompressible Navier-Stokes problem totally discretized in time and space, in two dimensions, by a two-grid method. In the first part, we extend the two-grid method, applied by V. Girault and J.-L. Lions to the transient semi-discretized Navier-Stokes problem, to the totally discretized Navier-Stokes probl...
Article
Full-text available
In this Note, we study a two-grid scheme fully discrete in time and space for solving the Navier-Stokes system. In the first step, the fully non-linear problem is discretized in space on a coarse grid with mesh-size H and time step k. In the second step, the problem is discretized in space on a fine grid with mesh-size h and the same time step, and...
Article
Full-text available
In this paper we study the Stokes problem with some different boundary conditions. We establish a decoupled variational formulation into a system of velocity and a Poisson equation for the pressure. The continuous and corresponding discrete system do not need an inf-sup condition. Hence, the velocity is approximated with curl conforming finite elem...

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