Stabilized reduced order models for the advection-diffusion-reaction equation using operator splitting

DOI10.1016/j.camwa.2016.01.032zbMath1443.65216OpenAlexW2288548018MaRDI QIDQ2007281

Benjamin McLaughlin, Ming Ye, Janet S. Peterson

Publication date: 12 October 2020

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2016.01.032

zbMATH Keywords

operator splittingadvection-diffusion-reaction equationfinite element method (FEM)SUPGreduced order modeling (ROM)SOLD

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Initial-boundary value problems for second-order parabolic equations (35K20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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Uses Software

• SHASTA

Cites Work

• Stability of the SUPG finite element method for transient advection-diffusion problems
• Fully multidimensional flux-corrected transport algorithms for fluids
• On the definition of the SUPG parameter
• Stability of operator splitting methods for systems with indefinite operators: Advection-diffusion-reaction systems
• Proper orthogonal decomposition approach and error estimation of mixed finite element methods for the tropical Pacific Ocean reduced gravity model
• On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations. I: A review
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• Stabilized finite element methods. I.: Application to the advective- diffusive model
• Flux correction tools for finite elements
• SUPG reduced order models for convection-dominated convection-diffusion-reaction equations
• A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation
• Revisiting stabilized finite element methods for the advective-diffusive equation
• Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data
• Centroidal Voronoi Tessellations: Applications and Algorithms
• Centroidal Voronoi Tessellation-Based Reduced-Order Modeling of Complex Systems
• Flux-corrected transport. I: SHASTA, a fluid transport algorithm that works

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