Numerical analysis for a new non-conforming linear finite element on quadrilaterals

DOI10.1016/j.cam.2005.05.024zbMath1094.65117OpenAlexW1986152594MaRDI QIDQ2493919

Matthias Grajewski, Jaroslav Hron, Stefan Turek

Publication date: 16 June 2006

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.05.024

zbMATH Keywords

numerical examplesincompressible Navier-Stokes equationsfinite elementinf-sup conditioniterative solversKorn's inequalitynon-conforming elementelliptic second-order problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Navier-Stokes equations for incompressible viscous fluids (76D05) 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)

Related Items

\(P _{1}\)-nonconforming quadrilateral finite volume methods for the semilinear elliptic equations, Locally stabilized \(P_{1}\)-nonconforming quadrilateral and hexahedral finite element methods for the Stokes equations, A cheapest nonconforming rectangular finite element for the stationary Stokes problem, A unifying theory of a posteriori error control for nonconforming finite element methods

Uses Software

• FEATFLOW
• SPLIB

Cites Work

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• Dual weighted a posteriori error estimation for a new nonconforming linear finite element on quadrilaterals
• Simple nonconforming quadrilateral Stokes element
• Tools for simulating non‐stationary incompressible flow via discretely divergence‐free finite element models
• P₁-Nonconforming Quadrilateral Finite Element Methods for Second-Order Elliptic Problems
• Approximation by quadrilateral finite elements
• Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
• Multigrid methods for stabilized nonconforming finite elements for incompressible flow involving the deformation tensor formulation