A POD-BASED REDUCED-ORDER STABILIZED CRANK–NICOLSON MFE FORMULATION FOR THE NON-STATIONARY PARABOLIZED NAVIER–STOKES EQUATIONS

DOI10.3846/13926292.2015.1048758zbMath1488.65444OpenAlexW1862015658MaRDI QIDQ5011242

Zhen-Dong Luo

Publication date: 27 August 2021

Published in: Mathematical Modelling and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3846/13926292.2015.1048758

zbMATH Keywords

error estimateproper orthogonal decomposition methodnon-stationary parabolized Navier-Stokes equationsreduced-order stabilized Crank-Nicolson mixed finite element formulation

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical quadrature and cubature formulas (65D32) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Compressible Navier-Stokes equations (76N06)

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An optimized finite element extrapolating method for 2D viscoelastic wave equation ⋮ A reduced-order characteristic finite element method based on POD for optimal control problem governed by convection-diffusion equation ⋮ Reduced-order finite element approximation based on POD for the parabolic optimal control problem ⋮ An optimized SPDMFE extrapolation approach based on the POD technique for 2D viscoelastic wave equation ⋮ A stabilized MFE reduced-order extrapolation model based on POD for the 2D unsteady conduction-convection problem ⋮ A reduced-order finite element method based on POD for the incompressible miscible displacement problem ⋮ Numerical simulation for a incompressible miscible displacement problem using a reduced-order finite element method based on POD technique ⋮ A reduced-order Weak Galerkin finite element algorithm based on POD technique for parabolic problem on polytopal mesh ⋮ H2 OPTIMAL MODEL REDUCTION OF COUPLED SYSTEMS ON THE GRASSMANN MANIFOLD ⋮ A REDUCED-ORDER EXTRAPOLATION SPECTRAL-FINITE DIFFERENCE SCHEME BASED ON THE POD METHOD FOR 2D SECOND-ORDER HYPERBOLIC EQUATIONS

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