A mixed finite element method for the Stokes equations based on a weakly over-penalized symmetric interior penalty approach

DOI10.1007/s10915-013-9733-9zbMath1306.65276OpenAlexW1969353416MaRDI QIDQ461220

Andrew T. Barker, Susanne C. Brenner

Publication date: 10 October 2014

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-013-9733-9

zbMATH Keywords

convergenceparallel computationadaptive algorithmStokes problemmixed finite element methodnumerical resultadditive Schwarz preconditionersdiscontinuous finite element methodnonconforming meshesweakly over-penalized symmetric interior penalty method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Finite element methods applied to problems in fluid mechanics (76M10) Parallel numerical computation (65Y05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (8)

A parameter-free mixed formulation for the Stokes equations and linear elasticity with strongly symmetric stress ⋮ Generalized weak Galerkin methods for Stokes equations ⋮ A Posteriori Error Estimates of a Weakly Over-Penalized Symmetric Interior Penalty Method for Elliptic Eigenvalue Problems ⋮ A separation between the boundary shape and the boundary functions in the parametric integral equation system for the 3D Stokes equation ⋮ Error estimates of the weakly over-penalized symmetric interior penalty method for two variational inequalities ⋮ Piecewise $\mathbf {H^1}$ functions and vector fields associated with meshes generated by independent refinements ⋮ Forty Years of the Crouzeix‐Raviart element ⋮ Pressure recovery for weakly over-penalized discontinuous Galerkin methods for the Stokes problem

Cites Work

• Unnamed Item
• Unnamed Item
• Higher order weakly over-penalized symmetric interior penalty methods
• A posteriori error control for a weakly over-penalized symmetric interior penalty method
• An equal-order DG method for the incompressible Navier-Stokes equations
• An intrinsically parallel finite element method
• A weakly over-penalized symmetric interior penalty method for the biharmonic problem
• Two-level additive Schwarz preconditioners for a weakly over-penalized symmetric interior penalty method
• A weakly over-penalized symmetric interior penalty method
• A regularity result for the Stokes problem in a convex polygon
• Optimal adaptive nonconforming FEM for the Stokes problem
• Discontinuous finite element methods for incompressible flows on subdomains with non-matching interfaces
• Convergence and optimality of the adaptive nonconforming linear element method for the Stokes problem
• Stabilized discontinuous finite element approximations for Stokes equations
• Schwarz methods for a preconditioned WOPSIP method for elliptic problems
• Exponential convergence of mixed \(hp\)-DGFEM for Stokes flow in polygons
• A balancing domain decomposition by constraints preconditioner for a weakly over-penalized symmetric interior penalty method
• Quasi-Optimality of Adaptive Nonconforming Finite Element Methods for the Stokes Equations
• Penalty-Factor-Free Discontinuous Galerkin Methods for 2-Dim Stokes Problems
• Discontinuous Galerkin approximations of the Stokes and Navier-Stokes equations
• Analysis of HDG methods for Stokes flow
• Hybridized globally divergence-free LDG methods. Part I: The Stokes problem
• Piecewise divergence-free discontinuous Galerkin methods for Stokes flow
• Local and pointwise error estimates of the local discontinuous Galerkin method applied to the Stokes problem
• Finite Element Methods for Navier-Stokes Equations
• Mixed and Hybrid Finite Element Methods
• Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
• An analysis of the convergence of mixed finite element methods
• Mixedhp-DGFEM for Incompressible Flows
• Local Discontinuous Galerkin Methods for the Stokes System
• HP DISCONTINUOUS GALERKIN APPROXIMATIONS FOR THE STOKES PROBLEM
• A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems
• High-Resolution Conservative Algorithms for Advection in Incompressible Flow
• BUBBLE STABILIZED DISCONTINUOUS GALERKIN METHOD FOR STOKES' PROBLEM
• The Mathematical Theory of Finite Element Methods
• Analysis of a discontinuous Galerkin approximation of the Stokes problem based on an artificial compressibility flux
• Analysis and convergence of finite volume method using discontinuous bilinear functions
• Piecewise Solenoidal Vector Fields and the Stokes Problem

This page was built for publication: A mixed finite element method for the Stokes equations based on a weakly over-penalized symmetric interior penalty approach