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Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements

Ainsworth, M. and Rankin, R. (2008) Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements. SIAM Journal on Numerical Analysis, 46 (6). pp. 3207-3232. ISSN 0036-1429

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Abstract

We obtain a fully computable a posteriori error bound on the broken energy norm of the error in the nonconforming finite element approximation on triangles of arbitrary order of a linear second order elliptic problem with variable permeability. The estimator is completely free of unknown constants and provides a guaranteed numerical bound on the broken energy norm of the error. This estimator is shown to be efficient in the sense that it also provides a lower bound for the broken energy norm of the error up to a constant and higher order data oscillation terms