Unconditional stability and error estimates of modified characteristics FEMs for the Navier-Stokes equations

DOI10.1007/s00211-015-0767-9zbMath1346.76073OpenAlexW2299374223MaRDI QIDQ304526

Zhiyong Si, Jilu Wang, Sun, Weiwei

Publication date: 25 August 2016

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-015-0767-9

Mathematics Subject Classification ID

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) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61)

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Uses Software

• FreeFem++

Cites Work

• Unnamed Item
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• Second order modified method of characteristics mixed defect-correction finite element method for time dependent Navier-Stokes problems
• An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable
• 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
• A characteristic/finite element algorithm for time-dependent 3-D advection-dominated transport using unstructured grids.
• A second order characteristic finite element scheme for convection-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
• Modified Lagrange-Galerkin methods of first and second order in time for convection-diffusion problems
• Modified characteristics gauge-Uzawa finite element method for time dependent conduction-convection problems
• Pointwise error estimates of finite element approximations to the Stokes problem on convex polyhedra
• Unconditional Convergence and Optimal Error Estimates of a Galerkin-Mixed FEM for Incompressible Miscible Flow in Porous Media
• Error analysis of linearized semi-implicit Galerkin finite element methods for nonlinear parabolic equations
• Superconvergent HDG Methods on Isoparametric Elements for Second-Order Elliptic Problems
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• An Optimal-Order Error Estimate for a Family of ELLAM-MFEM Approximations to Porous Medium Flow
• A Finite Element Alternating-Direction Method Combined with a Modified Method of Characteristics for Convection-Diffusion Problems
• Some Improved Error Estimates for the Modified Method of Characteristics
• A Modified Characteristic Finite Element Method for a Fully Nonlinear Formulation of the Semigeostrophic Flow Equations
• An efficient second-order characteristic finite element method for non-linear aerosol dynamic equations
• Finite Element Methods for Navier-Stokes Equations
• 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
• 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
• Curved Elements in the Finite Element Method. I
• 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
• Computing with hp-ADAPTIVE FINITE ELEMENTS
• The Stability and Convergence of Fully Discrete Galerkin-Galerkin FEMs for Porous Medium Flows
• Stability and Convergence of the Crank–Nicolson/Adams–Bashforth scheme for the Time‐Dependent Navier–Stokes Equations
• Numerical Analysis of Convection‐Diffusion‐Reaction Problems with Higher Order Characteristics/Finite Elements. Part I: Time Discretization
• Numerical Analysis of Convection‐Diffusion‐Reaction Problems with Higher Order Characteristics/Finite Elements. Part II: Fully Discretized Scheme and Quadrature Formulas
• On error estimates of some higher order penalty-projection methods for 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

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