# Hyam AbboudLebanese University · Faculty of Science

Hyam Abboud

PhD

## About

12

Publications

1,841

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110

Citations

Citations since 2017

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 (12)

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...