A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation

Authors:
Mark Ainsworth
Affiliations:
-
Venue:
SIAM Journal on Numerical Analysis
Year:
2007

Citing 0
Cited 17

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Abstract

It is shown that the interelement discontinuities in a discontinuous Galerkin finite element approximation are subordinate to the error measured in the broken $H^1$-seminorm. One consequence is that the DG-norm of the error is equivalent to the broken energy seminorm. Computable a posteriori error bounds are obtained for the error measured in both the DG-norm and the broken energy seminorm and are shown to be efficient in the sense that they also provide lower bounds up to a constant and higher order data oscillation terms. The estimators are completely free of unknown constants and provide guaranteed numerical bounds for the error.