Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem

Authors:
C. Carstensen;C. Merdon
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

Citing 12
Cited 1

A posteriori L2-error estimates for the nonconforming P1/P0-finite element discretization of the Stokes equations

Journal of Computational and Applied Mathematics
Explicit Error Bounds for a Nonconforming Finite Element Method

SIAM Journal on Numerical Analysis
Fully Reliable Localized Error Control in the FEM

SIAM Journal on Scientific Computing
Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis

Numerische Mathematik
A Local A Posteriori Error Estimator Based on Equilibrated Fluxes

SIAM Journal on Numerical Analysis
Robust A Posteriori Error Estimation for Nonconforming Finite Element Approximation

SIAM Journal on Numerical Analysis
A unifying theory of a posteriori finite element error control

Numerische Mathematik
A Posteriori Error Estimates for Lowest-Order Mixed Finite Element Discretizations of Convection-Diffusion-Reaction Equations

SIAM Journal on Numerical Analysis
A Posteriori Error Estimation for Lowest Order Raviart-Thomas Mixed Finite Elements

SIAM Journal on Scientific Computing
Fully Computable Bounds for the Error in Nonconforming Finite Element Approximations of Arbitrary Order on Triangular Elements

SIAM Journal on Numerical Analysis
Convergence of a standard adaptive nonconforming finite element method with optimal complexity

Applied Numerical Mathematics
Guaranteed and Fully Robust a posteriori Error Estimates for Conforming Discretizations of Diffusion Problems with Discontinuous Coefficients

Journal of Scientific Computing

Fully computable a posteriori error estimates for the Stokes equation without the global inf-sup constant

Computers & Mathematics with Applications

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Abstract

This paper compares different a posteriori error estimators for nonconforming first-order Crouzeix-Raviart finite element methods for simple second-order partial differential equations. All suggested error estimators yield a guaranteed upper bound of the discrete energy error up to oscillation terms with explicit constants. Novel equilibration techniques and an improved interpolation operator for the design of conforming approximations of the discrete nonconforming finite element solution perform very well in an error estimator competition with six benchmark examples.