Abstract
We present in this paper a rigorous error analysis of the vector penalty-projection method for solving the time-dependent incompressible Stokes equations with open boundary conditions on part of the boundary.
First, we prove the stability of the scheme.
Then we provide an error analysis for the second-order vector penalty-projection method which shows that the convergence rate of the error on the velocity and the pressure is of order 2 in
References
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- In Memoriam of Raytcho Lazarov
- A Finite Element Analysis in Balanced Norms for a Coupled System of Singularly Perturbed Reaction-Diffusion Equations
- Analysis of a Combined Spherical Harmonics and Discontinuous Galerkin Discretization for the Boltzmann Transport Equation
- On Error Estimates of a Discontinuous Galerkin Method of the Boussinesq System of Equations
- Finite Element Formulations for Maxwell’s Eigenvalue Problem Using Continuous Lagrangian Interpolations
- Variational Approximation for a Non-Isothermal Coupled Phase-Field System: Structure-Preservation & Nonlinear Stability
- Error Analysis of the Vector Penalty-Projection Methods for the Time-Dependent Stokes Equations with Open Boundary Conditions
- Numerical Analysis of a Second-Order Algorithm for the Time-Dependent Natural Convection Problem
- A Space-Time Finite Element Method for the Eddy Current Approximation of Rotating Electric Machines
- A P 2 H-Div-Nonconforming-H-Curl Finite Element for the Stokes Equations on Triangular Meshes
- An Inverse Matrix Eigenvalue Problem for Constructing a Vibrating Rod
- Anisotropic Adaptive Finite Elements for a p-Laplacian Problem
- On an Optimal AFEM for Elastoplasticity
Artikel in diesem Heft
- Frontmatter
- In Memoriam of Raytcho Lazarov
- A Finite Element Analysis in Balanced Norms for a Coupled System of Singularly Perturbed Reaction-Diffusion Equations
- Analysis of a Combined Spherical Harmonics and Discontinuous Galerkin Discretization for the Boltzmann Transport Equation
- On Error Estimates of a Discontinuous Galerkin Method of the Boussinesq System of Equations
- Finite Element Formulations for Maxwell’s Eigenvalue Problem Using Continuous Lagrangian Interpolations
- Variational Approximation for a Non-Isothermal Coupled Phase-Field System: Structure-Preservation & Nonlinear Stability
- Error Analysis of the Vector Penalty-Projection Methods for the Time-Dependent Stokes Equations with Open Boundary Conditions
- Numerical Analysis of a Second-Order Algorithm for the Time-Dependent Natural Convection Problem
- A Space-Time Finite Element Method for the Eddy Current Approximation of Rotating Electric Machines
- A P 2 H-Div-Nonconforming-H-Curl Finite Element for the Stokes Equations on Triangular Meshes
- An Inverse Matrix Eigenvalue Problem for Constructing a Vibrating Rod
- Anisotropic Adaptive Finite Elements for a p-Laplacian Problem
- On an Optimal AFEM for Elastoplasticity