<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we present a posteriori analysis of the discretization of the heat equation by spectral element method. We apply Euler’s implicit scheme in time and spectral method in space. We propose two families of error indicators both of them are built from the residual of the equation and we prove that they satisfy some optimal estimates. We present some numerical results which are coherent with the theoretical ones.</p></abstract>

In this paper, we present a posteriori analysis of the discretization of the heat equation by spectral element method. We apply Euler’s implicit scheme in time and spectral method in space. We propose two families of error indicators both of them are built from the residual of the equation and we prove that they satisfy some optimal estimates. We present some numerical results which are coherent with the theoretical ones.

A posteriori analysis of the spectral element discretization of heat equation

Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.

Département de Mathématique, Faculté des Sciences de Tunis, Campus Universitaire 1060 Tunis, Tunisie.

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"A posteriori analysis of the spectral element discretization of heat equation"}

In this paper, we present a posteriori analysis of the discretization of the heat equation by spectral element method. We apply Euler’s implicit scheme in time...

A posteriori analysis of the spectral element discretization of heat equation

Published Online: Dec 22, 2015

Page range: 13 - 36

Received: May 01, 2013

Accepted: Jul 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0047

Keywords
Heat equation, Spectral elements discretization, Error indicators

© 2014 Nejmeddine Chorfi et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A posteriori analysis of the spectral element discretization of heat equation

Published Online: Dec 22, 2015

Page range: 13 - 36

Received: May 01, 2013

Accepted: Jul 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0047

KeywordsHeat equation, Spectral elements discretization, Error indicators

© 2014 Nejmeddine Chorfi et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Heat equation, Spectral elements discretization, Error indicators