Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A Posteriori Error Estimators for the Raviart--Thomas Element
SIAM Journal on Numerical Analysis
Explicit Error Bounds for a Nonconforming Finite Element Method
SIAM Journal on Numerical Analysis
Some Nonoverlapping Domain Decomposition Methods
SIAM Review
Explicit error bounds in a conforming finite element method
Mathematics of Computation
Reliable Methods for Computer Simulation: Error Control and a Posteriori Estimates
Reliable Methods for Computer Simulation: Error Control and a Posteriori Estimates
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 Posteriori Error Estimation for Lowest Order Raviart-Thomas Mixed Finite Elements
SIAM Journal on Scientific Computing
Recovery-Based Error Estimator for Interface Problems: Conforming Linear Elements
SIAM Journal on Numerical Analysis
A Note on Constant-Free A Posteriori Error Estimates
SIAM Journal on Numerical Analysis
Recovery-Based Error Estimators for Interface Problems: Mixed and Nonconforming Finite Elements
SIAM Journal on Numerical Analysis
Flux Recovery and A Posteriori Error Estimators: Conforming Elements for Scalar Elliptic Equations
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
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This paper analyzes an equilibrated residual a posteriori error estimator for the diffusion problem. The estimator, which is a modification of those in [D. Braess and J. Schöberl, Math. Comput., 77 (2008), pp. 651-672; R. Verfürth, SIAM J. Numer. Anal., 47 (2009), pp. 3180-3194], is based on the Prager-Synge identity and on a local recovery of an equilibrated flux. Numerical results for an interface test problem show that the modification is necessary for the robustness of the estimator. When the distribution of diffusion coefficients is local quasi-monotone, it is shown theoretically that the estimator is robust with respect to the size of jumps.