Banach space projections and Petrov–Galerkin estimates [PDF]
Numerische Mathematik, 2014 9 pages; v2: added new section on application to Lp and Sobolev ...
Stern, Ari
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On the stability of projection methods for the incompressible Navier-Stokes equations based on high-order discontinuous Galerkin discretizations [PDF]
Journal of Computational Physics, 2017 The present paper deals with the numerical solution of the incompressible Navier–Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space.
Niklas Fehn, W. Wall, M. Kronbichler
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Coarse‐graining molecular dynamics models using an extended Galerkin projection method [PDF]
International Journal for Numerical Methods in Engineering, 2014 SUMMARYWe present a new framework for coarse‐graining molecular dynamics models for crystalline solids. The reduction method is based on a Galerkin projection to a subspace, whose dimension is much smaller than that of the full atomistic model. To effectively reduce artificial reflections of phonons at the interface, we construct extended subspaces ...
Xiantao Li
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Conservative interpolation between volume meshes by local Galerkin projection
Computer Methods in Applied Mechanics and Engineering, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Farrell, P, Maddison, J
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Rapid convergence of a Galerkin projection of the KdV equation
Comptes Rendus. Mathématique, 2005 In this Note, it is shown that a Fourier Galerkin approximation of the Korteweg–de Vries equation with periodic boundary conditions converges exponentially fast if the initial data can be continued analytically to a strip about the real axis.
H. Kalisch
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Full state approximation by Galerkin projection reduced order models for stochastic and bilinear systems [PDF]
Applied Mathematics and Computation, 2021 In this paper, the problem of full state approximation by model reduction is studied for stochastic and bilinear systems. Our proposed approach relies on identifying the dominant subspaces based on the reachability Gramian of a system.
Martin Redmann, I. P. Duff
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EXPLORING TRANSIENT, NEUTRONIC, REDUCED-ORDER MODELS USING DMD/POD-GALERKIN AND DATA-DRIVEN DMD [PDF]
EPJ Web of Conferences, 2021 There is growing interest in the development of transient, multiphysics models for nuclear reactors and analysis of uncertainties in those models. Reduced-order models (ROMs) provide a computationally cheaper alternative to compute uncertainties. However,
Elzohery Rabab, Roberts Jeremy
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Chaotic systems learning with hybrid echo state network/proper orthogonal decomposition based model
Data-Centric Engineering, 2021 We explore the possibility of combining a knowledge-based reduced order model (ROM) with a reservoir computing approach to learn and predict the dynamics of chaotic systems.
Mathias Lesjak, Nguyen Anh Khoa Doan
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Journal of Modern Power Systems and Clean Energy, 2021 In power systems, there are many uncertainty factors such as power outputs of distributed generations and fluctuations of loads. It is very beneficial to power system analysis to acquire an explicit function describing the relationship between these ...
Hao Wu +5 more
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Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems
Journal of Mathematical Sciences and Modelling, 2023 Shigesada-Kawasaki-Teramoto (SKT) is the most known equation in population ecology for nonlinear cross-diffusion systems. The full order model (FOM) of the SKT system is constructed using symmetric interior penalty discontinuous Galerkin method (SIPG ...
Gülden Mülayim
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