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Toufic El Arwadi

Publications and source records attributed to Toufic El Arwadi.

5 recordsLinked to original sources
arXiv2026

A Priori and A Posteriori Error Estimates for a Crank Nicolson Type Scheme of an Elliptic Problem with Dynamical Boundary Conditions

In this article we claim that we are going to give a priori and a posteriori error estimates for a Crank Nicolson type scheme. The problem is discretized by the finite elements in space. The main result of this paper consists in establishing two types of error indicators, the first one linked to the time discretization and the second one to the space discretization.

math.NA↗
arXiv2025

Exponential decay of the discrete energy for the wave-wave coupled system

In this article, a numerical analysis of the asymptotic behavior of the discrete energy associated to a dissipative coupled wave system is conducted. The numerical approximation of the system is constructed using the P1 finite element method for spatial discretization, combined with the implicit Euler scheme for time integration. An a priori error analysis is established, showing that, under extra regularity assumptions on the continuous solution, the numerical scheme exhibits linear convergence. Then, for the first time in the literature, the exponential decay of the fully discrete energy is shown using the energy method.

math.NA↗
arXiv2022

Energy decay analysis for Porous elastic system with microtemperature : A second spectrum approach

In this work, we analyze porous elastic system with microtemperature from second spectrum viewpoint. Indeed, by using the classical Faedo-Galerkin method combined with the a priori estimates, we prove the existence and uniqueness of a global solution of this problem. Then we prove that this solution is exponentially stable without assuming the condition of equal wave speeds. Then, we introduce a finite element approximation and we prove that the associated discrete energy decays. Finally, we obtain some a priori error estimates assuming additional regularity on the solution and we present some numerical results which demonstrate the accuracy of the approximation and the behaviour of the solution

math.AP↗
arXiv2020

Bresse-Timoshenko type systems with thermodiffusion effects: Well-possedness, stability and numerical results

Bresse-Timoshenko beam model with thermal, mass diffusion and theormoelastic effects is studied. We state and prove the well-posedness of problem. The global existence and uniqueness of the solution is proved by using the classical Faedo-Galerkin approximations along with two a priori estimates. We prove an exponential stability estimate for problem under an unusual assumption, and by using a multiplier technique in two different cases, with frictional damping in the angular rotation and with frictional damping in the vertical displacement. In numerical parts, we first obtained a numerical scheme for problem by $P_1$-finite element method for space discretization and implicit Euler scheme for time discretization. Then, we showed that the discrete energy decays, later a priori error estimates are established. Finally , some numerical simulations are presented.

math.AP↗