A Priori and A Posteriori Pseudostress-velocity Mixed Finite Element Error Analysis for the Stokes Problem

DOI10.1137/100816237zbMath1232.65098OpenAlexW2110507293MaRDI QIDQ3116418

Carsten Carstensen, Dongho Kim, Eun-Jae Park

Publication date: 22 February 2012

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/241241e405e4a28b55d5e649811a394e2ec594ee

zbMATH Keywords

Stokes problem a posteriori error estimates mixed finite element approximations pseudostress-velocity formulation

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) 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)

Related Items (35)

Domain decomposition and expanded mixed method for parabolic partial differential equations ⋮ Error estimates of pseudostress-velocity MFEM for optimal control problems governed by Stokes equations ⋮ Novel adaptive hybrid discontinuous Galerkin algorithms for elliptic problems ⋮ An a posteriori error estimate for a dual mixed method applied to Stokes system with non-null source terms ⋮ A multiscale domain decomposition approach for parabolic equations using expanded mixed method ⋮ Guaranteed a posteriori error estimates for a staggered discontinuous Galerkin method ⋮ Axioms of adaptivity ⋮ Superconvergent pseudostress-velocity finite element methods for the Oseen equations ⋮ Analysis of a mixed DG method for stress-velocity formulation of the Stokes equations ⋮ A Staggered Discontinuous Galerkin Method of Minimal Dimension on Quadrilateral and Polygonal Meshes ⋮ Error analysis for the pseudostress formulation of unsteady Stokes problem ⋮ An adaptive discontinuous Galerkin method for the Darcy system in fractured porous media ⋮ A priori error estimates of multiblock mortar expanded mixed method for elliptic problems ⋮ Optimal error estimates for the pseudostress formulation of the Navier-Stokes equations ⋮ Nonconforming finite element methods of order two and order three for the Stokes flow in three dimensions ⋮ A parameter-free mixed formulation for the Stokes equations and linear elasticity with strongly symmetric stress ⋮ A Unified Analysis of Quasi-Optimal Convergence for Adaptive Mixed Finite Element Methods ⋮ Three First-Order Finite Volume Element Methods for Stokes Equations under Minimal Regularity Assumptions ⋮ Staggered DG Methods for the Pseudostress-Velocity Formulation of the Stokes Equations on General Meshes ⋮ Analysis of multiscale mortar mixed approximation of nonlinear elliptic equations ⋮ Superconvergence analysis and two-grid algorithms of pseudostress-velocity MFEM for optimal control problems governed by Stokes equations ⋮ Quasi-optimal adaptive mixed finite element methods for controlling natural norm errors ⋮ Space-time adaptive methods for the mixed formulation of a linear parabolic problem ⋮ A staggered DG method of minimal dimension for the Stokes equations on general meshes ⋮ An adaptive least-squares FEM for the Stokes equations with optimal convergence rates ⋮ Fully computable bounds for a staggered discontinuous Galerkin method for the Stokes equations ⋮ Convergence of multi-level algorithms for a class of nonlinear problems ⋮ The norm of a discretized gradient in \(H(\mathrm{div})^*\) for a posteriori finite element error analysis ⋮ A new hybrid staggered discontinuous Galerkin method on general meshes ⋮ Computation of the LBB Constant for the Stokes Equation with a Least-Squares Finite Element Method ⋮ Multiscale mortar mixed domain decomposition approximations of nonlinear parabolic equations ⋮ Guaranteed velocity error control for the pseudostress approximation of the Stokes equations ⋮ Error estimates for a vorticity-based velocity-stress formulation of the Stokes eigenvalue problem ⋮ Comparison results for the Stokes equations ⋮ The enriched Crouzeix-Raviart elements are equivalent to the Raviart-Thomas elements

This page was built for publication: A Priori and A Posteriori Pseudostress-velocity Mixed Finite Element Error Analysis for the Stokes Problem