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Kumar, Sarvesh; Ruiz-Baier, Ricardo

Equal order discontinuous finite volume element methods for the Stokes problem. (English) Zbl 1330.76085

J. Sci. Comput. 65, No. 3, 956-978 (2015).
Summary: 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 \(L^2\)-norm under the assumption that the source term is locally in \(H^1\). Several numerical experiments in two and three spatial dimensions are presented to validate our theoretical findings.

Cited in 17 Documents

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
65N08 Finite volume methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
76D07 Stokes and related (Oseen, etc.) flows
65N15 Error bounds for boundary value problems involving PDEs

Keywords:

Stokes equations; discontinuous Galerkin methods; stabilization; finite volume element methods; error analysis
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References:

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