A PRIORI AND A POSTERIORI OF A LINEAR ELLIPTIC PROBLEM WITH DYNAMICAL BOUNDARY CONDITION.

Toufic El Arwadi (1) , Séréna Dib (2) , Toni Sayah (3)

1 Department of mathematics
2 FS - Faculté des sciences-USJ
3 Département de Mathématiques, Université Sainnt-Jseph, Liban

In this paper, we study the time dependent linear elliptic problem with dynamical boundary condition. The problem is discretized by the backward Euler's scheme in time and finite elements in space. In this work, an optimal a priori error estimate is established and an optimal a posteriori errors with two types of computable error indicators is proved. The first one being linked to the time discretization and the second one to the space discretization. Using these a posteriori errors estimates, an adaptative algorithm for computing the solution is proposed. Finally, numerical experiments are presented to show the efectiveness of the obtained error estimators and the proposed adaptive algorithm.

Mots clés: Dynamic boundary condition; nite element method; a posteriori analysis

Domaines: Analyse numérique [math.NA]

Toufic El Arwadi, Séréna Dib, Toni Sayah. A PRIORI AND A POSTERIORI OF A LINEAR ELLIPTIC PROBLEM WITH DYNAMICAL BOUNDARY CONDITION.. 2015. ⟨hal-01054311v2⟩