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Variational multiscale proper orthogonal decomposition: convection-dominated convection-diffusion-reaction equations. (English) Zbl 06190116
Summary: We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested for convection-dominated convection-diffusion-reaction equations. The numerical analysis of the finite element discretization of the model is presented. Numerical tests show the increased numerical accuracy over the standard reduced-order model and illustrate the theoretical convergence rates.
MSC:
76F65Direct numerical and large eddy simulation of turbulence
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
76F20Dynamical systems approach to turbulence
65M15Error bounds (IVP of PDE)