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A new local projection stabilization virtual element method for the Oseen problem on polygonal meshes

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Abstract

For the Oseen problem, we present a new stabilized virtual element method on polygonal meshes that allows us to employ “equal-order” virtual element pairs to approximate both velocity and pressure. By introducing the local projection type stabilization terms to the virtual element method, the method can not only circumvent the discrete Babuška-Brezzi condition, but also maintain the favorable stability and approximation properties of residual-based stabilization methods. In particular, it does not need to calculate complex high-order derivative terms and avoids the strong coupling terms of velocity and pressure. Error estimates are obtained without depending on the inverse of the viscosity, which means that the method is effective in the convective-dominated regime. Some numerical experiments are performed to verify the method has good behaviors.

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Acknowledgements

In particular, our deepest gratitude goes to the anonymous reviewers for their careful work and thoughtful suggestions that have helped improve this paper substantially.

Funding

This research was supported by the National Nature Science Foundation of China (No. 11971337), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11901078) and the Fundamental Research Funds for the Central Universities (Grant No. ZYGX2020J021).

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Authors and Affiliations

  1. College of Mathematics, Sichuan University, 610065, Chengdu, China

    Yang Li & Minfu Feng

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, 611731, Chengdu, China

    Yan Luo

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  1. Yang Li
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  2. Minfu Feng
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  3. Yan Luo
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Correspondence to Minfu Feng.

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Communicated by: Lourenco Beirao da Veiga

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Li, Y., Feng, M. & Luo, Y. A new local projection stabilization virtual element method for the Oseen problem on polygonal meshes. Adv Comput Math 48, 30 (2022). https://doi.org/10.1007/s10444-022-09952-4

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