Unilateral problem for the Stokes equations: the well-posedness and finite element approximation

DOI10.1016/j.apnum.2016.03.002zbMath1381.76201OpenAlexW2187024945MaRDI QIDQ278791

Guanyu Zhou, Yoshiki Sugitani, Norikazu Saito

Publication date: 2 May 2016

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2016.03.002

zbMATH Keywords

finite element approximationStokes equationsunilateral boundary condition

Mathematics Subject Classification ID

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 element methods applied to problems in fluid mechanics (76M10)

Related Items (10)

Analysis of Stokes system with solution-dependent subdifferential boundary conditions ⋮ The Navier-Stokes equations under a unilateral boundary condition of Signorini's type ⋮ Steady flow with unilateral and leak/slip boundary conditions by the Stokes variational–hemivariational inequality ⋮ Constrained evolutionary variational-hemivariational inequalities with application to fluid flow model ⋮ A new class of variational‐hemivariational inequalities for steady Oseen flow with unilateral and frictional type boundary conditions ⋮ A new class of generalized quasi-variational inequalities with applications to Oseen problems under nonsmooth boundary conditions ⋮ Energy Inequalities and Outflow Boundary Conditions for the Navier–Stokes Equations ⋮ Numerical computation of blood flow for a patient-specific hemodialysis shunt model ⋮ A new class of elliptic quasi-variational-hemivariational inequalities for fluid flow with mixed boundary conditions ⋮ An inverse problem for Bingham type fluids

Cites Work

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• The Navier-Stokes equations under a unilateral boundary condition of Signorini's type
• Semi-discrete stabilized finite element methods for Navier-Stokes equations with nonlinear slip boundary conditions based on regularization procedure
• Cardiovascular mathematics. Modeling and simulation of the circulatory system
• Functional analysis, Sobolev spaces and partial differential equations
• Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device
• The stability in L\(^q\) of the L\(^2\)-projection into finite element function spaces
• Mathematical tools for the study of the incompressible Navier-Stokes equations and related models
• A mixed formulation for the Signorini problem in nearly incompressible elasticity
• Finite element modeling of blood in arteries
• On convergence of the penalty method for unilateral contact problems
• Outflow boundary conditions for the incompressible non-homogeneous Navier-Stokes equations
• Estimates for the \(L_{2}\)-projection onto continuous finite element spaces in a weighted \(L_{p }\)-norm
• Finite Element Method for Stokes Equations under Leak Boundary Condition of Friction Type
• Error estimates for Stokes problem with Tresca friction conditions
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Finite Element Methods for Navier-Stokes Equations
• The Stability in L p and W p 1 of the L 2 -Projection onto Finite Element Function Spaces
• Effective downstream boundary conditions for incompressible Navier–Stokes equations
• Mixed Finite Element Methods and Applications
• Optimal Convergence for Discrete Variational Inequalities Modelling Signorini Contact in 2D and 3D without Additional Assumptions on the Unknown Contact Set
• The Mathematical Theory of Finite Element Methods
• ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS
• New efficient boundary conditions for incompressible Navier-Stokes equations : a well-posedness result

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