Uniform Bounds with Difference Quotients for Proper Orthogonal Decomposition Reduced Order Models of the Burgers Equation

Abstract

In this paper, we prove uniform error bounds for proper orthogonal decomposition (POD) reduced order modeling (ROM) of Burgers equation, considering difference quotients (DQs), introduced in Kunisch and Volkwein (Numer Math 90(1):117–148, 2001). In particular, we study the behavior of the DQ ROM error bounds by considering L2(Ω) and H10(Ω) POD spaces and l∞(L2) and natural-norm errors. We present some meaningful numerical tests checking the behavior of error bounds.