An exactly computable Lagrange–Galerkin scheme for the Navier–Stokes equations and its error estimates

DOI10.1090/mcom/3222zbMath1452.76102OpenAlexW2536797996MaRDI QIDQ4586611

Masahisa Tabata, Shinya Uchiumi

Publication date: 30 October 2017

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/mcom/3222

zbMATH Keywords

finite element methodnumerical stabilityTaylor-Hood elementlocally linearized velocity

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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

A mass-preserving two-step Lagrange-Galerkin scheme for convection-diffusion problems ⋮ Lagrange nodal discontinuous Galerkin method for fractional Navier-Stokes equations ⋮ Behavior of Lagrange‐Galerkin solutions to the Navier‐Stokes problem for small time increment ⋮ Error estimates of a stabilized Lagrange−Galerkin scheme for the Navier−Stokes equations ⋮ A viscosity-independent error estimate of a pressure-stabilized Lagrange-Galerkin scheme for the Oseen problem ⋮ Second-Order Finite Difference Approximations of the Upper-Convected Time Derivative

Uses Software

• FreeFem++

Cites Work

• Unnamed Item
• Unnamed Item
• A genuinely stable Lagrange-Galerkin scheme for convection-diffusion problems
• A single-step characteristic-curve finite element scheme of second order in time for the incompressible Navier-Stokes equations
• Discrepancy between theory and real computation on the stability of some finite element schemes
• A stable finite element for the Stokes equations
• Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations
• Error estimates for finite element method solution of the Stokes problem in the primitive variables
• Exact projections and the Lagrange-Galerkin method: A realistic alternative to quadrature
• A second order characteristic finite element scheme for convection-diffusion problems
• On the transport-diffusion algorithm and its applications to the Navier-Stokes equations
• A vectorized particle tracer for unstructured grids
• Error estimates of a stabilized Lagrange−Galerkin scheme for the Navier−Stokes equations
• Stability and convergence of a Galerkin-characteristics finite element scheme of lumped mass type
• Error estimates for a mixed finite element approximation of the Stokes equations
• Numerical Integration Over Simplexes and Cones
• Modified Lagrange--Galerkin Methods to Integrate Time Dependent Incompressible Navier--Stokes Equations
• Finite Element Methods for Navier-Stokes Equations
• Stability of the Lagrange-Galerkin method with non-exact integration
• Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures
• Some criteria for numerically integrated matrices and quadrature formulas for triangles
• A high-order characteristics/finite element method for the incompressible Navier-Stokes equations
• A Second Order in Time Modified Lagrange--Galerkin Finite Element Method for the Incompressible Navier--Stokes Equations
• New development in freefem++
• Convergence Analysis of a Finite Element Projection/Lagrange--Galerkin Method for the Incompressible Navier--Stokes Equations
• Error Estimates of a Stabilized Lagrange–Galerkin Scheme of Second-Order in Time for the Navier–Stokes Equations