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Journal of Scientific Computing

Erschienen in:

01.10.2020

A New Projection-Based Stabilized Virtual Element Method for the Stokes Problem

verfasst von: Jun Guo, Minfu Feng

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2020

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Abstract

We propose and analyze a stabilized virtual element method for the Stokes problem on polytopal meshes. We employ the \(C^0\) continuous arbitrary “equal-order” virtual element pairs to approximate both velocity and pressure, and develop a projection-based stabilization term to circumvent the discrete inf-sup condition, then we obtain the corresponding error estimates. The presented method involves neither the projection of the second derivative nor additional coupling terms, and it is parameter-free. In particularly, for the lowest-order case on triangular (tetrahedral) meshes the stabilized method introduced by Bochev et al. (SIAM J. Numer. Anal. 44: 82–101, 2006) is a special case of our method up to an approximation of the load term. Furthermore, numerical results are shown to confirm the theoretical predictions.

Vorheriger Artikel Semi-implicit Hermite–Galerkin Spectral Method for Distributed-Order Fractional-in-Space Nonlinear Reaction–Diffusion Equations in Multidimensional Unbounded Domains

Nächster Artikel Compact Schemes for Multiscale Flows with Cell-Centered Finite Difference Method

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Titel: A New Projection-Based Stabilized Virtual Element Method for the Stokes Problem
verfasst von: Jun Guo
Minfu Feng
Publikationsdatum: 01.10.2020
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2020
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01301-1

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