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

McLaughlin, Benjamin; Peterson, Janet; Ye, Ming

doi:10.1016/j.camwa.2016.01.032

Title: Stabilized reduced order models for the advection–diffusion–reaction equation using operator splitting

Journal Article · Wed Jun 01 00:00:00 EDT 2016 · Computers and Mathematics with Applications (Oxford)

DOI:https://doi.org/10.1016/j.camwa.2016.01.032· OSTI ID:1631363

McLaughlin, Benjamin; Peterson, Janet; Ye, Ming

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0009324

OSTI ID:: 1631363

Alternate ID(s):: OSTI ID: 1351653

Journal Information:: Computers and Mathematics with Applications (Oxford), Journal Name: Computers and Mathematics with Applications (Oxford) Vol. 71 Journal Issue: 11; ISSN 0898-1221

Publisher:: ElsevierCopyright Statement

Country of Publication:: United Kingdom

Language:: English

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Cited by: 9 works

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References (17)

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Fully multidimensional flux-corrected transport algorithms for fluids Zalesak, Steven T. Journal of Computational Physics, Vol. 31, Issue 3 https://doi.org/10.1016/0021-9991(79)90051-2	journal	June 1979
Reduced Basis Technique for Nonlinear Analysis of Structures Noor, Ahmed K.; Peters, Jeanne M. AIAA Journal, Vol. 18, Issue 4 https://doi.org/10.2514/3.50778	journal	April 1980
Flux Correction Tools for Finite Elements Kuzmin, D.; Turek, S. Journal of Computational Physics, Vol. 175, Issue 2 https://doi.org/10.1006/jcph.2001.6955	journal	January 2002
Stability of the SUPG finite element method for transient advection–diffusion problems Bochev, Pavel B.; Gunzburger, Max D.; Shadid, John N. Computer Methods in Applied Mechanics and Engineering, Vol. 193, Issue 23-26 https://doi.org/10.1016/j.cma.2004.01.026	journal	June 2004
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations Brooks, Alexander N.; Hughes, Thomas J. R. Computer Methods in Applied Mechanics and Engineering, Vol. 32, Issue 1-3 https://doi.org/10.1016/0045-7825(82)90071-8	journal	September 1982
SUPG reduced order models for convection-dominated convection–diffusion–reaction equations Giere, Swetlana; Iliescu, Traian; John, Volker Computer Methods in Applied Mechanics and Engineering, Vol. 289 https://doi.org/10.1016/j.cma.2015.01.020	journal	June 2015
Revisiting stabilized finite element methods for the advective–diffusive equation Franca, Leopoldo P.; Hauke, Guillermo; Masud, Arif Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issue 13-16 https://doi.org/10.1016/j.cma.2005.05.028	journal	February 2006
A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation Codina, Ramon Computer Methods in Applied Mechanics and Engineering, Vol. 110, Issue 3-4 https://doi.org/10.1016/0045-7825(93)90213-H	journal	December 1993
Stability of operator splitting methods for systems with indefinite operators: Advection–diffusion–reaction systems Ropp, David L.; Shadid, John N. Journal of Computational Physics, Vol. 228, Issue 9 https://doi.org/10.1016/j.jcp.2009.02.001	journal	May 2009
On spurious oscillations at layers diminishing (SOLD) methods for convection–diffusion equations: Part I – A review John, Volker; Knobloch, Petr Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 17-20 https://doi.org/10.1016/j.cma.2006.11.013	journal	March 2007
Centroidal Voronoi Tessellations: Applications and Algorithms Du, Qiang; Faber, Vance; Gunzburger, Max SIAM Review, Vol. 41, Issue 4 https://doi.org/10.1137/S0036144599352836	journal	January 1999
Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data Gunzburger, Max D.; Peterson, Janet S.; Shadid, John N. Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 4-6 https://doi.org/10.1016/j.cma.2006.08.004	journal	January 2007
Stabilized finite element methods: I. Application to the advective-diffusive model Franca, Leopoldo P.; Frey, Sergio L.; Hughes, Thomas J. R. Computer Methods in Applied Mechanics and Engineering, Vol. 95, Issue 2 https://doi.org/10.1016/0045-7825(92)90143-8	journal	March 1992
Centroidal Voronoi Tessellation-Based Reduced-Order Modeling of Complex Systems Burkardt, John; Gunzburger, Max; Lee, Hyung-Chun SIAM Journal on Scientific Computing, Vol. 28, Issue 2 https://doi.org/10.1137/5106482750342221x	journal	January 2006
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