A Priori and a Posteriori Error Estimates of a WOPSIP DG Method for the Heat Equation-Reference-Cited by-同舟云学术

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

Published:2020-04-17 Issue: Volume:2020 Page:1-11
ISSN:1024-123X
Container-title:Mathematical Problems in Engineering
language:en
Short-container-title:Mathematical Problems in Engineering

Author:

Zeng Yuping¹^ORCID,Wen Kunwen¹^ORCID,Liang Fen¹,Zhu Huijian²

Affiliation:

1. School of Mathematics, Jiaying University, Meizhou 514015, China

2. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, Guangxi 537000, China

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.

Funder

Natural Science Foundation of Guangdong Province

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Link

http://downloads.hindawi.com/journals/mpe/2020/7525676.pdf

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