Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 65, Issue 3, Pages 956-978Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-015-9993-7
Keywords
Stokes equations; Discontinuous Galerkin methods; Stabilization; Finite volume element methods; Error analysis
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Funding
- University of Lausanne
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The aim of this paper is to develop and analyze a family of stabilized discontinuous finite volume element methods for the Stokes equations in two and three spatial dimensions. The proposed scheme is constructed using a baseline finite element approximation of velocity and pressure by discontinuous piecewise linear elements, where an interior penalty stabilization is applied. A priori error estimates are derived for the velocity and pressure in the energy norm, and convergence rates are predicted for velocity in the -norm under the assumption that the source term is locally in . Several numerical experiments in two and three spatial dimensions are presented to validate our theoretical findings.
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