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A Posteriori Error Estimates for Maxwell Equations

Joachim Schöberl
Mathematics of Computation
Vol. 77, No. 262 (Apr., 2008), pp. 633-649
Stable URL: http://www.jstor.org/stable/40234527
Page Count: 17
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A Posteriori Error Estimates for Maxwell Equations
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Abstract

Maxwell equations are posed as variational boundary value problems in the function space H (curl) and are discretized by Nédélec finite elements. In Beck et al., 2000, a residual type a posteriori error estimator was proposed and analyzed under certain conditions onto the domain. In the present paper, we prove the reliability of that error estimator on Lipschitz domains. The key is to establish new error estimates for the commuting quasi-interpolation operators recently introduced in J. Schöberl, Commuting quasi-interpolation operators for mixed finite elements. Similar estimates are required for additive Schwarz preconditioning. To incorporate boundary conditions, we establish a new extension result.

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