A unified stabilized finite volume method for Stokes and Darcy equations

DOI10.4134/JKMS.j180641zbMath1428.65060OpenAlexW2967417963MaRDI QIDQ5242995

N. Kechkar, Akram Boukabache

Publication date: 8 November 2019

Full work available at URL: https://www.kci.go.kr/kciportal/ci/sereArticleSearch/ciSereArtiView.kci?sereArticleSearchBean.artiId=ART002475373

zbMATH Keywords

finite volumesStokes equationDarcy equationstabilized methodscollocated discretizations

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Error bounds for boundary value problems involving PDEs (65N15) Stokes and related (Oseen, etc.) flows (76D07) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite volume methods for boundary value problems involving PDEs (65N08)

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Cites Work

• A stabilized finite volume method for Stokes equations using the lowest order \(P_1-P_0\) element pair
• A new finite element formulation for computational fluid dynamics. VII. The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces
• On a stabilized colocated Finite Volume scheme for the Stokes problem
• A posteriori error estimates of stabilized finite volume method for the Stokes equations
• Unified Stabilized Finite Element Formulations for the Stokes and the Darcy Problems
• Finite Element Methods for Navier-Stokes Equations
• Analysis of Locally Stabilized Mixed Finite Element Methods for the Stokes Problem
• A Robust Finite Element Method for Darcy--Stokes Flow
• Unified Analysis of Finite Volume Methods for the Stokes Equations
• Stabilized Crouzeix‐Raviart element for the Darcy‐Stokes problem
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