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Date
2020-06Type
- Report
ETH Bibliography
yes
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Abstract
We analyse the p- and hp-versions of the virtual element method (VEM) for the the Stokes problem on a polygonal domain. The key tool in the analysis is the existence of a bijection between Poisson-like and Stokes-like VE spaces for the velocities. This allows us to re-interpret the standard VEM for Stokes as a VEM, where the test and trial discrete velocities are sought in Poisson-like VE spaces. The upside of this fact is that we inherit from [Beirão da Veiga, L., Chernov, A., Mascotto, L., Russo, A.: Exponential convergence of the hp virtual element method with corner singularity. Numer. Math. 138(3), 581–613 (2018)] an explicit analysis of best interpolation results in VE spaces, as well as stabilization estimates that are explicit in terms of the degree of accuracy of the method. We prove exponential convergence of the hp-VEM for Stokes problems with regular right-hand sides. We corroborate the theoretical estimates with numerical tests for both the p- and hp-versions of the method. Show more
Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
Stokes equation; virtual element methods; polygonal meshes; p- and hp- Galerkin methodsOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
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