A Priori and a Posteriori Error Analysis for a Linear Elliptic Problem with Dynamic Boundary Condition

Authors

Toufic El Arwadi, Department of Mathematics and computer science, Faculty of Science, Beirut Arab university, P.O. Box: 11-5020, Beirut, LebanonFollow
Séréna DIB, Unité de recherche EGFEM, Faculté des Sciences, Université Saint-Joseph, B.P 11-514 Riad El Solh, Beyrouth 1107 2050, LibanFollow
Toni Sayah, Unité de recherche EGFEM, Faculté des Sciences, Université Saint-Joseph, B.P 11-514 Riad El Solh, Beyrouth 1107 2050, LibanFollow

Author Country (or Countries)

Lebanon

Abstract

In this paper, we study the time dependent linear elliptic problem with dynamic 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 error with two types of computable error indicators is proved. The first one is linked to the time discretization and the second one to the space discretization. Using these a posteriori errors estimates, an adaptive algorithm for computing the solution is proposed. Finally, numerical experiments are presented to show the effectiveness of the obtained error estimators and the proposed adaptive algorithm.

Recommended Citation

El Arwadi, Toufic; DIB, Séréna; and Sayah, Toni (2015) "A Priori and a Posteriori Error Analysis for a Linear Elliptic Problem with Dynamic Boundary Condition," Applied Mathematics & Information Sciences: Vol. 09: Iss. 6, Article 58.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss6/58