Error estimators for nonconforming finite element approximations of the Stokes problem
Mathematics of Computation
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
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 Discontinuous Galerkin 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
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Applied Numerical Mathematics
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We give an overview of our recent progress in developing a framework for the derivation of fully computable guaranteed posteriori error bounds for finite element approximation including conforming, non-conforming, mixed and discontinuous finite element schemes. Whilst the details of the actual estimator are rather different for each particular scheme, there is nonetheless a common underlying structure at work in all cases. We aim to illustrate this structure by treating conforming, non-conforming and discontinuous finite element schemes in a single framework. In taking a rather general viewpoint, some of the finer details of the analysis that rely on the specific properties of each particular scheme are obscured but, in return, we hope to allow the reader to 'see the wood despite the trees'.