Title

HDG-POD Reduced Order Model of the Heat Equation

Abstract

We propose a new hybridizable discontinuous Galerkin (HDG) model order reduction technique based on proper orthogonal decomposition (POD). We consider the heat equation as a test problem and prove error bounds that converge to zero as the number of POD modes increases. We present 2D and 3D numerical results to illustrate the convergence analysis.

Department(s)

Mathematics and Statistics

Comments

J. Singler and Y. Zhang were supported in part by National Science Foundation, United States, grant DMS-1217122. J. Singler and Y. Zhang thank the Institute for Mathematics and its Applications at the University of Minnesota for funding research visits, during which some of this work was completed. The authors thank Bernardo Cockburn for many helpful conversations.
Article in Press

Keywords and Phrases

Error analysis; Heat transfer; Partial differential equations; Principal component analysis; Convergence analysis; Discontinuous galerkin; Discontinuous Galerkin methods; Heat equation; Model order reduction; Numerical results; Proper orthogonal decompositions; Reduced order models; Galerkin methods; Hybridizable discontinuous Galerkin method

International Standard Serial Number (ISSN)

0377-0427

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2018 Elsevier, All rights reserved.

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