Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics

By Karl Kunisch, Stefan Volkwein. SIAM Journal on Numerical Analysis, 2002

788 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e961b6e5ba1437af98b8dc583cdcbb68cc95e9c6

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Citations in the corpus

Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Parabolic PDEs: Application to Real‐Time Bayesian Parameter Estimation (2010, methodology): “To begin, we summarize the well-known optimality property of the POD as described in Kunisch and Volkwein (2002) .”
Finite element formulation based on proper orthogonal decomposition for parabolic equations (2009, methodology): “Though Kunisch and Volkwein [16, 17 ] have combined the POD method with Galerkin method”
Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations (2007, methodology): “Section 11.2 for non-compliant problems we discuss (primal-dual [117]) RB Galerkin projection [121] and optimality; in Section 7.2 we describe (briefly) POD methods [8,24,58, 73 ] and (more extensively) greedy sampling procedures [32,33,153] for optimal space identification; in Section 8.1 for one p”
Computational Reduction for Parametrized PDEs: Strategies and Applications (2012, background): “The first applications of POD were concerned with the analysis of turbulent flows and date back to the early ’90s [1, 2]; more recent applications can be found, for instance, in [22,25,27,30], as well as in [9, 12,20] for parametrized flows.”
A New Selection Operator for the Discrete Empirical Interpolation Method - Improved A Priori Error Bound and Extensions (2015, background): “For more details on POD, we refer the reader to [28, 32].”
Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation (2009, background): “To begin, we summarize the wellknown optimality property of the POD [22].”
Port reduction in parametrized component static condensation: approximation and a posteriori error estimation (2013, methodology): “†† We then perform a data compression step: we invoke the proper orthogonal decomposition (POD) [21] (with respect to the L(2) p inner product).”
Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair (2013, methodology): “The POD methods, in combination with the Galerkin projection procedure, have also provided an efficient means for generating reduced-order models [6] [7] [8].”
Model Order Reduction of Differential Algebraic Equations Arising from the Simulation of Gas Transport Networks (2014, background): “The following lemma is a known result see for example [KV02].”
Using adaptive proper orthogonal decomposition to solve the reaction--diffusion equation (2007, background): “Another approach to bounding model errors is presented in [ 21 ].”
Comparison of the reduced-basis and POD a posteriori error estimators for an elliptic linear-quadratic optimal control problem (2011, background): “In [13] the dependence of {ψi} i=1 and {λi} i=1 for ≤ 2n on the chosen snapshot grid f is investigated.”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, background): “A priori error estimates for POD approximations were introduced in [72] and can be used to gauge the total number of POD modes to retain to achieve a given representation accuracy at one single parameter point.”
A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations (2010, methodology): “…is classically used as an a posteriori model reduction technique for long-time simulations or parametric analyses of evolution problems [5] [4] [19] [20] [16] [36] [24] [10] [15] [3] In this paper, we focus on the more challenging problem of the a priori construction of such separated…”
POD-Galerkin method for finite volume approximation of Navier–Stokes and RANS equations (2016, methodology): “In this subsection, the classic POD-G-ROM methodology is briefly summarized according to [11,22,23,54].”