HDG-POD Reduced Order Model of the Heat Equation
arXiv:1801.0007922 citationsh-index: 16
AI Analysis
This work provides a theoretical foundation for HDG-POD reduced order models in heat transfer, but is incremental as it applies existing techniques to a standard problem.
The paper proposes a hybridizable discontinuous Galerkin reduced order model using proper orthogonal decomposition for the heat equation, proving convergent error bounds and demonstrating convergence in 2D and 3D numerical tests.
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.