Computer Methods in Applied Mechanics and Engineering
Edge Residuals Dominate A Posteriori Error Estimates for Low Order Finite Element Methods
SIAM Journal on Numerical Analysis
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 unifying theory of a posteriori error control for nonconforming finite element methods
Numerische Mathematik
Framework for the A Posteriori Error Analysis of Nonconforming Finite Elements
SIAM Journal on Numerical Analysis
A posteriori error estimates for the Steklov eigenvalue problem
Applied Numerical Mathematics
Spectral approximation of variationally-posed eigenvalue problems by nonconforming methods
Journal of Computational and Applied Mathematics
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This paper deals with a posteriori error estimators for the non conforming Crouzeix-Raviart finite element approximations of the Steklov eigenvalue problem. First, we define an error estimator of the residual type which can be computed locally from the approximate eigenpair and we prove the equivalence between this estimator and the broken energy norm of the error with constants independent of the corresponding eigenvalue. Next, we prove that edge residuals dominate the volumetric part of the residual and that the volumetric part of the residual terms dominate the normal component of the jumps of the discrete fluxes across interior edges. Finally, based on these results, we introduce two simpler equivalent error estimators. The analysis shows that these a posteriori error estimates are optimal up to higher order terms and that may be used for the design of adaptive algorithms.