Finite element approximation for the viscoelastic fluid motion problem

DOI10.1016/S0377-0427(02)00864-6zbMath1014.76041OpenAlexW2154615457MaRDI QIDQ1811584

Robert Tait, Yin-Nian He, Yan Ping Lin, Sun, Weiwei, Samuel Shan-Pu Shen

Publication date: 17 June 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(02)00864-6

zbMATH Keywords

regularityerror estimatespressurevariational formulationfinite element approximationvelocityuniqueness conditiontwo-dimensional viscoelastic fluid motion

Mathematics Subject Classification ID

Viscoelastic fluids (76A10) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (23)

Optimal error estimates for semidiscrete Galerkin approximations to equations of motion described by Kelvin-Voigt viscoelastic fluid flow model ⋮ Finite element penalty method for the Oldroyd model of order one with non-smooth initial data ⋮ Fully discrete second-order backward difference method for Kelvin-Voigt fluid flow model ⋮ Crank-Nicolson extrapolation and finite element method for the Oldroyd fluid with the midpoint rule ⋮ On error estimates of the penalty method for the viscoelastic flow problem. I: Time discretization ⋮ Long time error estimates of IFE methods for the unsteady multi-layer porous wall model ⋮ Fully discrete finite element error analysis of a discontinuous Galerkin method for the Kelvin-Voigt viscoelastic fluid model ⋮ A viscoelastic Timoshenko beam model: regularity and numerical approximation ⋮ Stabilized finite element method for the viscoelastic Oldroyd fluid flows ⋮ Well-posedness and invariant measures for 2D stochastic Oldroyd model of order one with pure jumps ⋮ On a three step two‐grid finite element method for the Oldroyd model of order one ⋮ Two-grid finite element Galerkin approximation of equations of motion arising in Oldroyd fluids of order one with non-smooth initial data ⋮ Unnamed Item ⋮ A finite element penalty method for the linearized viscoelastic Oldroyd fluid motion equations ⋮ Unnamed Item ⋮ A gauge-Uzawa finite element method for the time-dependent viscoelastic Oldroyd flows ⋮ Optimal error analysis of Crank-Nicolson schemes for a coupled nonlinear Schrödinger system in 3D ⋮ An incremental pressure correction finite element method for the time-dependent Oldroyd flows ⋮ Semidiscrete Galerkin method for equations of motion arising in Kelvin‐Voigt model of viscoelastic fluid flow ⋮ A large time stepping viscosity-splitting finite element method for the viscoelastic flow problem ⋮ The stabilized penalty-projection finite element method for the Navier-Stokes-Cahn-Hilliard-Oono system ⋮ Deterministic and stochastic equations of motion arising in Oldroyd fluids of order one: existence, uniqueness, exponential stability and invariant measures ⋮ Fully discrete finite element method based on second-order Crank-Nicolson/Adams-Bashforth scheme for the equations of motion of Oldroyd fluids of order one

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A modified nonlinear Galerkin method for the viscoelastic fluid motion equations
• On mathematical models of a viscoelasticity with a memory
• Error estimates for finite element method solution of the Stokes problem in the primitive variables
• Finite element approximation of the Navier-Stokes equations. Rev. repr. of the 1st ed
• An error estimate uniform in time for spectral Galerkin approximations of the Navier-Stokes problem
• Fluid dynamics of viscoelastic liquids
• A regularity result for the Stokes problem in a convex polygon
• Nonlinear Galerkin methods and mixed finite elements: Two-grid algorithms for the Navier-Stokes equations
• On the global existence and convergence to steady state of Navier-Stokes flow past an obstacle that is started from rest
• Convergence and stability of finite element nonlinear Galerkin method for the Navier-Stokes equations
• On the convergence of viscoelastic fluid flows to a steady state
• A Conforming Finite Element Method for the Time-Dependent Navier–Stokes Equations
• Finite Element Approximation of the Nonstationary Navier–Stokes Problem, Part II: Stability of Solutions and Error Estimates Uniform in Time
• Finite Element Approximation of the Nonstationary Navier–Stokes Problem. I. Regularity of Solutions and Second-Order Error Estimates for Spatial Discretization
• Motion of nonlinear visco-elastic fluid
• Approximation of the global attractor for the incompressible Navier-Stokes equations
• Two-Grid Discretization Techniques for Linear and Nonlinear PDE<scp>s</scp>
• Error Estimates on a New Nonlinear Galerkin Method Based on Two-Grid Finite Elements
• Asymptotics of Stable Viscoelastic Fluid Motion (Oldroyd's Mathematical Model)
• Postprocessing the Galerkin Method: The Finite-Element Case
• On a Linearized Backward Euler Method for the Equations of Motion of Oldroyd Fluids of Order One

This page was built for publication: Finite element approximation for the viscoelastic fluid motion problem