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Advances in Mathematical Physics
Volume 2017, Article ID 9736818, 11 pages
https://doi.org/10.1155/2017/9736818
Research Article

Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients

1Department of Mathematics, Korea Military Academy, Hwarangro 564, Seoul 01805, Republic of Korea
2Department of Mathematics, Korea University, Anamro 145, Seoul 02841, Republic of Korea

Correspondence should be addressed to Hyung Kyu Jun; rk.ca.amk@7230nujkh

Received 11 November 2016; Revised 24 March 2017; Accepted 11 April 2017; Published 3 May 2017

Academic Editor: Kaliyaperumal Nakkeeran

Copyright © 2017 Minam Moon et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

HDG method has been widely used as an effective numerical technique to obtain physically relevant solutions for PDE. In a practical setting, PDE comes with nonlinear coefficients. Hence, it is inevitable to consider how to obtain an approximate solution for PDE with nonlinear coefficients. Research on using HDG method for PDE with nonlinear coefficients has been conducted along with results obtained from computer simulations. However, error analysis on HDG method for such settings has been limited. In this research, we give error estimations of the hybridizable discontinuous Galerkin (HDG) method for parabolic equations with nonlinear coefficients. We first review the classical HDG method and define notions that will be used throughout the paper. Then, we will give bounds for our estimates when nonlinear coefficients obey “Lipschitz” condition. We will then prove our main result that the errors for our estimations are bounded.