A posteriori error estimates for a Maxwell type problem

I. Anjam, O. Mali, A. Muzalevsky, P. Neittaanmäki, S. Repin
2009 Russian Journal of Numerical Analysis and Mathematical Modelling  
In this paper, we discuss a posteriori estimates for the Maxwell type boundary-value problem. The estimates are derived by transformations of integral identities that define the generalized solution and are valid for any conforming approximation of the exact solution. It is proved analytically and confirmed numerically that the estimates indeed provide a computable and guaranteed bound of approximation errors. Also, it is shown that the estimates imply robust error indicators that represent the
more » ... distribution of local (inter-element) errors measured in terms of different norms. Here Ω is a bounded and connected domain in d with the Lipschitz boundary ∂ Ω, and J is the applied current. Using the constituent relations ¡
doi:10.1515/rjnamm.2009.025 fatcat:nrgtiucmmfcgjhbfcxhkpb7ofu