An a posteriori error estimate and a comparison theorem for the nonconforming \(P_{1}\) element

DOI10.1007/s10092-009-0003-zzbMath1192.65142OpenAlexW2121179843MaRDI QIDQ734127

Dietrich Braess

Publication date: 19 October 2009

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10092-009-0003-z

zbMATH Keywords

finite elementa posteriori error estimatesPoisson equationCrouzeix-Raviart elementhypercircle methodnonconforming \(P_1\) elementRaviard-Thomas element

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) 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 (14)

An Adaptive Multilevel Monte Carlo Method with Stochastic Bounds for Quantities of Interest with Uncertain Data ⋮ Projection stabilized nonconforming finite element methods for the stokes problem ⋮ Four closely related equilibrated flux reconstructions for nonconforming finite elements ⋮ Efficient Discrete Lagrange Multipliers in three first-order finite element discretizations for the A Posteriori Error Control in an Obstacle Problem ⋮ Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem ⋮ Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems ⋮ Nonconforming discretizations of convex minimization problems and precise relations to mixed methods ⋮ The Prager–Synge theorem in reconstruction based a posteriori error estimation ⋮ Aspects of Guaranteed Error Control in CPDEs ⋮ Forty Years of the Crouzeix‐Raviart element ⋮ Comparison Results of NonstandardP₂Finite Element Methods for the Biharmonic Problem ⋮ A posteriori error analysis for nonconforming approximations of an anisotropic elliptic problem ⋮ Comparison results for the Stokes equations ⋮ The enriched Crouzeix-Raviart elements are equivalent to the Raviart-Thomas elements

Cites Work

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• Equilibrated residual error estimates are \(p\)-robust
• A Posteriori Error Estimation for Lowest Order Raviart–Thomas Mixed Finite Elements
• An Inexpensive Method for the Evaluation of the Solution of the Lowest Order Raviart–Thomas Mixed Method
• A posteriori error estimators for nonconforming finite element methods
• Approximations in elasticity based on the concept of function space
• Finite Elements

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