A right-inverse for divergence operator in spaces of piecewise polynomials. Application to the p-version of the finite element method
From MaRDI portal
Publication:1836289
DOI10.1007/BF01396303zbMath0504.65060OpenAlexW2339151134MaRDI QIDQ1836289
Publication date: 1983
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/132837
finite element methodLaplace equationStokes problemoptimal convergencedivergence operatormaximal right-inverse
Finite element methods applied to problems in solid mechanics (74S05) Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)
Related Items
Small-scale divergence penalization for incompressible flow problems via time relaxation ⋮ Quasioptimality of some spectral mixed methods ⋮ Stable finite element pair for Stokes problem and discrete Stokes complex on quadrilateral grids ⋮ The \(p\) and \(h-p\) versions of some finite element methods for Stokes' problem ⋮ Unlocking the secrets of locking: finite element analysis in planar linear elasticity ⋮ The Scott-Vogelius finite elements revisited ⋮ The Leray-\(\alpha\beta\)-deconvolution model: energy analysis and numerical algorithms ⋮ Analytical and computational assessment of locking in the \(hp\) finite element method ⋮ Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials ⋮ A P4 bubble enriched P3 divergence-free finite element on triangular grids ⋮ Crouzeix-Raviart triangular elements are inf-sup stable ⋮ On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows ⋮ The inf-sup constant for \textit{hp}-Crouzeix-Raviart triangular elements ⋮ Exact sequences on Worsey–Farin splits ⋮ A pressure-robust mixed finite element method for the coupled Stokes-Darcy problem ⋮ Statically Condensed Iterated Penalty Method for High Order Finite Element Discretizations of Incompressible Flow ⋮ A locking-free weak Galerkin finite element method for linear elasticity problems ⋮ Enforcing energy, helicity and strong mass conservation in finite element computations for incompressible Navier-Stokes simulations ⋮ A numerical study of the Navier-Stokes-\(\alpha \beta \) model ⋮ Collision in a cross-shaped domain - A steady 2D Navier-Stokes example demonstrating the importance of mass conservation in CFD ⋮ A sensitivity study of the Navier-Stokes-\(\alpha\) model ⋮ On computing the pressure by the \(p\) version of the finite element method for Stokes problem ⋮ Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes-problem ⋮ A Banach spaces-based analysis of a new fully-mixed finite element method for the Boussinesq problem ⋮ \(p\)-version of mixed finite element methods for Stokes-like problems ⋮ Locking effects in the finite element approximation of elasticity problems ⋮ Unnamed Item ⋮ Divergence stability in connection with the $p$-version of the finite element method ⋮ Non-nested multi-grid solvers for mixed divergence-free scott-vogelius discretizations ⋮ On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime ⋮ Cubic Lagrange elements satisfying exact incompressibility ⋮ Mass Conserving Mixed $hp$-FEM Approximations to Stokes Flow. Part I: Uniform Stability ⋮ An analysis of the p-version of the finite element method for nearly incompressible materials. Uniformly valid, optimal error estimates ⋮ Efficient linear solvers for incompressible flow simulations using Scott-Vogelius finite elements ⋮ The Stokes complex: A review of exactly divergence–free finite element pairs for incompressible flows ⋮ A subgrid stabilization finite element method for incompressible magnetohydrodynamics ⋮ Discrete and conforming smooth de Rham complexes in three dimensions ⋮ The p- and h-p versions of the finite element method. An overview ⋮ Adaptive finite elements for flow problems with moving boundaries. I. Variational principles and a posteriori estimates ⋮ Numerical study of the Navier–Stokes-αdeconvolution model with pointwise mass conservation
Cites Work
- Unnamed Item
- Unnamed Item
- Direct and inverse error estimates for finite elements with mesh refinements
- On mixed finite element methods for first order elliptic systems
- Error estimates for the combined h and p versions of the finite element method
- Nodal variables for complete conforming finite elements of arbitrary polynomial order
- An analysis of the p-version of the finite element method for nearly incompressible materials. Uniformly valid, optimal error estimates
- A Projection Method Applied to Diffusion in a Periodic Structure
- Thep-Version of the Finite Element Method
- A Nodal Basis for C 1 Piecewise Polynomials of Degree n ≥5
- An Analysis of the Finite Element Method Using Lagrange Multipliers for the Stationary Stokes Equations
- A Finite Element Method for the Stationary Stokes Equations Using Trial Functions which do not have to Satisfy div u= 0
- A note on an inequality of E. Schmidt