Publication de 6 numéros par an
ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352
Indexed in
Multiscale and Residual-Free Bubble Functions for Reaction-Advection-Diffusion Problems
RÉSUMÉ
We propose a finite element method based on enriching the Galerkin approximation spaces with a combination of multiscale functions and residual-free bubbles (RFB). This approach is presented as a Petrov-Galerkin method and applied to the singularly perturbed reaction-advection-diffusion model. Numerical tests confirm that switching RFB by suitable multiscale functions in the elements connected to the outflow boundaries of the domain improves the accuracy of the solution in this region.
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Franca L. P., Ramalho J. V. A., Valentin F., Enriched finite element methods for unsteady reaction-diffusion problems, Communications in Numerical Methods in Engineering, 22, 6, 2005. Crossref
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Barrenechea Gabriel R., Franca Leopoldo P., Valentin Frédéric, A Symmetric Nodal Conservative Finite Element Method for the Darcy Equation, SIAM Journal on Numerical Analysis, 47, 5, 2009. Crossref
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Bochev Pavel B., Gunzburger Max D., Lehoucq Richard B., On stabilized finite element methods for the Stokes problem in the small time step limit, International Journal for Numerical Methods in Fluids, 53, 4, 2007. Crossref
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Gravemeier V., The variational multiscale method for laminar and turbulent flow, Archives of Computational Methods in Engineering, 13, 2, 2006. Crossref
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Hsieh Po-Wen, Yang Suh-Yuh, A Novel Least-Squares Finite Element Method Enriched with Residual-Free Bubbles for Solving Convection-Dominated Problems, SIAM Journal on Scientific Computing, 32, 4, 2010. Crossref
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Turner D. Z., Nakshatrala K. B., Hjelmstad K. D., A stabilized formulation for the advection-diffusion equation using the Generalized Finite Element Method, International Journal for Numerical Methods in Fluids, 66, 1, 2011. Crossref
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Hsieh Po-Wen, Yang Suh-Yuh, A bubble-stabilized least-squares finite element method for steady MHD duct flow problems at high Hartmann numbers, Journal of Computational Physics, 228, 22, 2009. Crossref
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Hachem E., Digonnet H., Kosseifi N., Massoni E., Coupez T., Enriched finite element spaces for transient conduction heat transfer, Applied Mathematics and Computation, 217, 8, 2010. Crossref
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Araya Rodolfo, Barrenechea Gabriel R., Franca Leopoldo P., Valentin Frédéric, Stabilization arising from PGEM: A review and further developments, Applied Numerical Mathematics, 59, 9, 2009. Crossref
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Ramirez Manuel, Moreles Miguel Angel, On the Finite Increment Calculus method for stabilizing advection-diffusion equations, analysis and computation of the stabilization parameter, International Journal for Numerical Methods in Fluids, 70, 3, 2012. Crossref
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Duan Huo-Yuan, Hsieh Po-Wen, Tan Roger C.E., Yang Suh-Yuh, Analysis of a new stabilized finite element method for the reaction–convection–diffusion equations with a large reaction coefficient, Computer Methods in Applied Mechanics and Engineering, 247-248, 2012. Crossref
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Baysal Onur, Bubble and multiscale stabilization of bilinear finite element methods for transient advection–diffusion equations on rectangular grids, Journal of Computational and Applied Mathematics, 259, 2014. Crossref
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Sendur A., Nesliturk A., Kaya A., Applications of the pseudo residual-free bubbles to the stabilization of the convection–diffusion–reaction problems in 2D, Computer Methods in Applied Mechanics and Engineering, 277, 2014. Crossref
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Duan Huoyuan, Qiu Fengjuan, A new stabilized finite element method for advection-diffusion-reaction equations, Numerical Methods for Partial Differential Equations, 32, 2, 2016. Crossref
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Hsieh Po-Wen, Yang Suh-Yuh, A new stabilized linear finite element method for solving reaction–convection–diffusion equations, Computer Methods in Applied Mechanics and Engineering, 307, 2016. Crossref
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Madureira Alexandre L., Two-Dimensional Reaction-Diffusion Equations, in Numerical Methods and Analysis of Multiscale Problems, 2017. Crossref
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Cheung Siu Wun, Guha Nilabja, Dynamic data-driven Bayesian GMsFEM, Journal of Computational and Applied Mathematics, 353, 2019. Crossref
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Carrillo Ruben, Moreles Miguel Angel, Herrera Rafael, Equivalence of DEC and box methods for the diffusion–advection–reaction equation, Boletín de la Sociedad Matemática Mexicana, 27, 2, 2021. Crossref
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ŞENDUR Ali, NATESAN Srinivasan, SINGH Gautam, Error estimates for a fully discrete $\varepsilon$-uniform finite element method on quasi uniform meshes, Hacettepe Journal of Mathematics and Statistics, 2021. Crossref
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Barrenechea Gabriel R., Valentin Frédéric, A residual local projection method for the Oseen equation, Computer Methods in Applied Mechanics and Engineering, 199, 29-32, 2010. Crossref