HDG-POD Reduced Order Model of the Heat Equation

TL;DR

This paper introduces a hybridizable discontinuous Galerkin (HDG) combined with proper orthogonal decomposition (POD) for reduced order modeling of the heat equation, demonstrating convergence and efficiency in 2D and 3D.

Contribution

It develops a novel HDG-POD reduced order model for the heat equation, with proven error bounds and numerical validation.

Findings

Error bounds converge to zero with more POD modes

Numerical results confirm theoretical convergence in 2D and 3D

Efficient reduced order modeling for 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.