Second order error bounds for POD-ROM methods based on first order divided differences

2023/06/06 by García-Archilla, Bosco, John, Volker, Novo, Julia
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2306.03550

Abstract

This note proves, for simplicity for the heat equation, that using BDF2 as time stepping scheme in POD-ROM methods with snapshots based on difference quotients gives both the optimal second order error bound in time and pointwise estimates.

Related

• On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal
• POD-ROM methods: error analysis for continuous parametrized approximations
• A new approach to proper orthogonal decomposition with difference quotients
• A New Proper Orthogonal Decomposition Method with Second Difference Quotients for the Wave Equation
• POD-ROM methods: from a finite set of snapshots to continuous-in-time approximations