A posteriori analysis of the spectral element discretization of a non linear heat equation

Abstract

The paper deals with a posteriori analysis of the spectral element discretization of a non linear heat equation. The discretization is based on Euler’s backward scheme in time and spectral discretization in space. Residual error indicators related to the discretization in time and in space are defined. We prove that those indicators are upper and lower bounded by the error estimation.

Keywords

• non linear heat equation
• spectral elements discretization
• error indicators
• a posteriori analysis
• 35j57
• 65m70