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Virtual element method stabilization for convection-diffusion-reaction problems using the link-cutting condition

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Abstract

In this paper, we present a methodology for stabilizing the virtual element method applied to the convection-diffusion-reaction equation. The stabilization is carried out modifying the mesh inside the boundary layer so that the link-cutting condition is satisfied. The method provides a stable solution to all regimes. Numerical examples are presented for several regimes in which satisfactory results are obtained.

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Acknowledgments

The author wishes to thank L. D. Marini, F. Brezzi, A. Russo and L. Beirão da Veiga for useful discussions. Also, the author gratefully thanks the Department of Mathematics of the University of Pavia for kind hospitality. This work has been partially funded by the Spanish MECD under FPU Grant AP210-2073, Gobierno de Aragón and FEDER funding from the European Union (Grupo Consolidado de Mecánica de Fluidos Computacional T21).

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  1. LIFTEC (CSIC)-Universidad de Zaragoza, Escuela de Ingeniería y Arquitectura, Área de Mecánica de Fluidos, C/María de Luna 3, 50018, Zaragoza, Spain

    D. Irisarri

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Irisarri, D. Virtual element method stabilization for convection-diffusion-reaction problems using the link-cutting condition. Calcolo 54, 141–154 (2017). https://doi.org/10.1007/s10092-016-0180-5

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  • DOI: https://doi.org/10.1007/s10092-016-0180-5

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