Unconditional optimal error estimate of the projection/Lagrange-Galerkin finite element method for the Boussinesq equations

DOI10.1007/s11075-019-00698-7zbMath1440.65148OpenAlexW2935935187WikidataQ128086688 ScholiaQ128086688MaRDI QIDQ2290925

Zhang Tong, Zhiyong Si, Yanfang Lei

Publication date: 29 January 2020

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-019-00698-7

zbMATH Keywords

Lagrange-Galerkin methodprojection finite element methodtime-dependent Boussinesq problemsunconditional optimal error estimate

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs (65M25) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11) Diffusive and convective heat and mass transfer, heat flow (80A19)

Related Items (6)

A Modified Characteristics Finite Element Method for the Electroneutral Micro-Fluids ⋮ A modified characteristic projection finite element method for the Kelvin-Voigt viscoelastic fluid equations ⋮ Unconditional superconvergence analysis of two modified finite element fully discrete schemes for nonlinear Burgers' equation ⋮ Decoupled Crank–Nicolson LeapFrog method for the evolution Boussinesq equations ⋮ Unconditional stability of first and second orders implicit/explicit schemes for the natural convection equations ⋮ Decoupled modified characteristic finite element method with different subdomain time steps for nonstationary dual-porosity-Navier-Stokes model

Uses Software

• FreeFem++

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unconditional stability and error estimates of modified characteristics FEMs for the Navier-Stokes equations
• A defect-correction method for unsteady conduction-convection problems. I: Spatial discretization
• A defect-correction mixed finite element method for stationary conduction-convection problems
• Finite difference methods for a nonlinear and strongly coupled heat and moisture transport system in textile materials
• Second order modified method of characteristics mixed defect-correction finite element method for time dependent Navier-Stokes problems
• A defect-correction method for unsteady conduction-convection problems. II: Time discretization
• Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations
• The characteristic streamline diffusion method for the time-dependent incompressible Navier-Stokes equations
• Characteristic mixed discontinuous finite element methods for advection-dominated diffusion problems
• Maximum-norm stability of the finite element Stokes projection
• On the transport-diffusion algorithm and its applications to the Navier-Stokes equations
• A high order characteristics method for the incompressible Navier-Stokes equations
• A locally conservative Eulerian--Lagrangian numerical method and its application to nonlinear transport in porous media
• Modified Lagrange-Galerkin methods of first and second order in time for convection-diffusion problems
• A simplified two-level method for the steady Navier-Stokes equations
• A Newton iterative mixed finite element method for stationary conduction–convection problems
• Pointwise error estimates of finite element approximations to the Stokes problem on convex polyhedra
• Error analysis of linearized semi-implicit Galerkin finite element methods for nonlinear parabolic equations
• Error analysis for finite element methods for steady natural convection problems
• An Optimal-Order Error Estimate for a Family of ELLAM-MFEM Approximations to Porous Medium Flow
• THE GAUGE-UZAWA FINITE ELEMENT METHOD PART II: THE BOUSSINESQ EQUATIONS
• Some Improved Error Estimates for the Modified Method of Characteristics
• An optimizing reduced PLSMFE formulation for non-stationary conduction-convection problems
• Time Stepping Along Characteristics with Incomplete Iteration for a Galerkin Approximation of Miscible Displacement in Porous Media
• Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures
• Implementation of the Lagrange‐Galerkin method for the incompressible Navier‐Stokes equations
• A high-order characteristics/finite element method for the incompressible Navier-Stokes equations
• Optimal error estimate of the penalty finite element method for the time-dependent Navier-Stokes equations
• Error Analysis for Characteristics-Based Methods for Degenerate Parabolic Problems
• A Characteristics-Mixed Finite Element Method for Advection-Dominated Transport Problems
• An Optimal-Order Estimate for Eulerian–Lagrangian Localized Adjoint Methods for Variable-Coefficient Advection-Reaction Problems
• 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
• A New Error Analysis of Characteristics-Mixed FEMs for Miscible Displacement in Porous Media
• Stability and Convergence of the Crank–Nicolson/Adams–Bashforth scheme for the Time‐Dependent Navier–Stokes Equations
• A characteristic-type formulation of the Navier-Stokes equations for high-order upwind schemes
• A summary of numerical methods for time-dependent advection-dominated partial differential equations
• A coupled Newton iterative mixed finite element method for stationary conduction-convection problems

This page was built for publication: Unconditional optimal error estimate of the projection/Lagrange-Galerkin finite element method for the Boussinesq equations