Error estimates on hybridizable discontinuous Galerkin methods for parabolic equations with nonlinear coefficients
type: Item
instance of: scholarly article
title: Error estimates on hybridizable discontinuous Galerkin methods for parabolic equations with nonlinear coefficients
zbMATH Open document ID: 1404.65129
DOI: 10.1155/2017/9736818
author: Hyung Kyu Jun
author: Tay Suh
author: M. Moon
published in: Advances in Mathematical Physics
publication date: 2018-10-23T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 6962694
zbMATH Keywords: hybridizable discontinuous Galerkin methods
zbMATH Keywords: error estimation
zbMATH Keywords: parabolic equations with nonlinear coefficients
Wikidata QID: Q59142487
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/9736818
OpenAlex ID: W2611728496
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description: scientific article; zbMATH DE number 6962694