Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations

DOI10.1016/j.camwa.2022.07.017OpenAlexW4289637111MaRDI QIDQ2172574

Volker John, Baptiste Moreau, Julia Novo

Publication date: 16 September 2022

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2022.07.017

zbMATH Keywords

error analysisa posteriori error estimationconvection-diffusion-reaction equationsconvection-dominated regimeSUPG-ROM method

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10) 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)

Related Items

On a certified VMS-Smagorinsky reduced basis model with LPS pressure stabilisation ⋮ A reduced-order immersed interface method based on POD basis for parabolic interface problem ⋮ POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order Solution

Uses Software

• UMFPACK
• ParMooN

Cites Work

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• An adaptive SUPG method for evolutionary convection-diffusion equations
• On the stability of the reduced basis method for Stokes equations in parametrized domains
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• SUPG reduced order models for convection-dominated convection-diffusion-reaction equations
• A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations
• On the convergence order of the finite element error in the kinetic energy for high Reynolds number incompressible flows
• A reduced order variational multiscale approach for turbulent flows
• ParMooN -- a modernized program package based on mapped finite elements
• Towards physically admissible reduced-order solutions for convection-diffusion problems
• Supremizer stabilization of POD-Galerkin approximation of parametrized steady incompressible Navier-Stokes equations
• Error Analysis of the SUPG Finite Element Discretization of Evolutionary Convection-Diffusion-Reaction Equations
• Numerical Analysis of a Projection-Based Stabilized POD-ROM for Incompressible Flows
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Turbulence and the dynamics of coherent structures. I. Coherent structures
• On a Certified Smagorinsky Reduced Basis Turbulence Model
• A streamline derivative POD-ROM for advection-diffusion-reaction equations
• Stabilization of Galerkin approximations of transport equations by subgrid modeling
• On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal Decomposition
• Error Analysis of Supremizer Pressure Recovery for POD based Reduced-Order Models of the Time-Dependent Navier--Stokes Equations
• Error Analysis of Proper Orthogonal Decomposition Stabilized Methods for Incompressible Flows
• Variational multiscale proper orthogonal decomposition: Navier‐stokes equations
• Algorithm 832
• Galerkin proper orthogonal decomposition methods for parabolic problems