Abstract
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.
Highlights
The a posteriori analysis technique presents a very e cient tool for the mesh adaptivity methods
The paper deals with a posteriori analysis of the spectral element discretization of a non linear heat equation
The spectral element method consists in approaching the solution of a partial di erential equation by polynomial function of high degree on each sub-domain of a decomposition
Summary
The a posteriori analysis technique presents a very e cient tool for the mesh adaptivity methods. We prove the optimality of those indicators in the sense that their Hilbertian sum is upper and lower bounded by the error estimation with constants independent of the discrete parameter in space and time.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
