A Priori and a Posteriori Error Estimates of a WOPSIP DG Method for the Heat Equation

Yuping Zeng, Kunwen Wen, Fen Liang and Huijian Zhu

Mathematical Problems in Engineering, 2020, vol. 2020, 1-11

Abstract:

We introduce and analyze a weakly overpenalized symmetric interior penalty method for solving the heat equation. We first provide optimal a priori error estimates in the energy norm for the fully discrete scheme with backward Euler time-stepping. In addition, we apply elliptic reconstruction techniques to derive a posteriori error estimators, which can be used to design adaptive algorithms. Finally, we present two numerical experiments to validate our theoretical analysis.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:7525676

DOI: 10.1155/2020/7525676

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