Local projection stabilization of equal order interpolation applied to the Stokes problem

DOI10.1090/S0025-5718-08-02130-3zbMath1198.65214MaRDI QIDQ3055058

Tobiska, Lutz, Sashikumaar Ganesan, Gunar Matthies

Publication date: 7 November 2010

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

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)

Related Items (33)

The two-grid stabilization of equal-order finite elements for the stokes equations ⋮ Supercloseness and superconvergence of stabilized low-order finite element discretizations of the Stokes Problem ⋮ A subgrid model for the time-dependent Navier-Stokes equations ⋮ A finite element variational multiscale method based on two-grid discretization for the steady incompressible Navier-Stokes equations ⋮ A three-step stabilized algorithm for the Navier-Stokes type variational inequality ⋮ Stabilization by local projection for convection-diffusion and incompressible flow problems ⋮ A two-level higher order local projection stabilization on hexahedral meshes ⋮ Local projection stabilized finite element methods for advection-reaction problems ⋮ Equal order discontinuous finite volume element methods for the Stokes problem ⋮ Acceleration of stabilized finite element discretizations for the Stokes eigenvalue problem ⋮ The two-level local projection stabilization as an enriched one-level approach ⋮ Equal-order finite elements with local projection stabilization for the Darcy-brinkman equations ⋮ A parallel stabilized finite element method based on the lowest equal-order elements for incompressible flows ⋮ Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations ⋮ Local projection stabilized Galerkin approximations for the generalized Stokes problem ⋮ A residual local projection method for the Oseen equation ⋮ A penalty finite element method for a fluid system posed on embedded surface ⋮ An overlapping local projection stabilization for Galerkin approximations of Stokes and Darcy flow problems ⋮ Analysis of Solving Galerkin Finite Element Methods with Symmetric Pressure Stabilization for the Unsteady Navier-Stokes Equations Using Conforming Equal Order Interpolation ⋮ Local and parallel stabilized finite element algorithms based on the lowest equal-order elements for the steady Navier-Stokes equations ⋮ A two-level local projection stabilisation on uniformly refined triangular meshes ⋮ A local projection stabilisation finite element method for the Stokes equations using biorthogonal systems ⋮ An equal-order hybridized discontinuous Galerkin method with a small pressure penalty parameter for the Stokes equations ⋮ A variational multi-scale method with spectral approximation of the sub-scales: application to the 1D advection-diffusion equations ⋮ Non-nested multi-grid solvers for mixed divergence-free scott-vogelius discretizations ⋮ A two-level finite element method for the stationary Navier-Stokes equations based on a stabilized local projection ⋮ Two-Level Defect-Correction Stabilized Finite Element Method for the Incompressible Navier–Stokes Equations Based on Pressure Projection ⋮ Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions ⋮ Higher-order discontinuous Galerkin time stepping and local projection stabilization techniques for the transient Stokes problem ⋮ Generalized local projection stabilized nonconforming finite element methods for Darcy equations ⋮ Edge patch-wise local projection stabilized nonconforming FEM for the Oseen problem ⋮ A reduced discrete inf-sup condition inL^pfor incompressible flows and application ⋮ Beyond pressure stabilization: A low-order local projection method for the Oseen equation

Uses Software

• MooNMD

Cites Work

• An efficient smoother for the Stokes problem
• MooNMD -- a program package based on mapped finite element methods
• A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations
• A modified streamline diffusion method for solving the stationary Navier- Stokes equation
• A stable finite element for the Stokes equations
• A new finite element formulation for computational fluid dynamics. VII. The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces
• Stabilized finite element methods. II: The incompressible Navier-Stokes equations
• A finite element formulation for the Stokes problem allowing equal velocity-pressure interpolation
• The quadrilateral `mini' finite element for the Stokes problem
• A finite element pressure gradient stabilization for the Stokes equations based on local projections
• The inf-sup condition for the mapped \(Q_k-P_{k-1}^{\text{disc}}\) element in arbitrary space dimensions
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Uniformly stable mixedhp-finite elements on multilevel adaptive grids with hanging nodes
• A unified convergence analysis for local projection stabilisations applied to the Oseen problem
• Finite Element Methods for Navier-Stokes Equations
• An Absolutely Stabilized Finite Element Method for the Stokes Problem
• Mixed and Hybrid Finite Element Methods
• L’élément $Q_1$-bulle/$Q_1$
• An Absolutely Stable Pressure-Poisson Stabilized Finite Element Method for the Stokes Equations
• Grad-div stablilization for Stokes equations
• Analysis of a Streamline Diffusion Finite Element Method for the Stokes and Navier–Stokes Equations
• Stabilization methods of bubble type for theQ₁/Q₁-element applied to the incompressible Navier-Stokes equations
• CONTINUOUS Q1–Q1 STOKES ELEMENTS STABILIZED WITH NON-CONFORMING NULL EDGE AVERAGE VELOCITY FUNCTIONS
• Local Projection Stabilization for the Oseen Problem and its Interpretation as a Variational Multiscale Method
• Mapped finite elements on hexahedra. Necessary and sufficient conditions for optimal interpolation errors
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