Robust A Posteriori Error Estimation for Finite Element Approximation to H(curl) Problem
This work provides a robust error estimation method for computational electromagnetics, addressing a known bottleneck in finite element analysis of H(curl) problems with inhomogeneous media.
The paper introduces a novel recovery-type a posteriori error estimator for conforming finite element approximations to the H(curl) problem with inhomogeneous media and L^2 right-hand side. The estimator is proven to be approximately equal to the true error in the energy norm without the quasi-monotonicity assumption, and numerical results for two interface problems demonstrate its effectiveness.
In this paper, we introduce a novel a posteriori error estimator for the conforming finite element approximation to the H(curl) problem with inhomogeneous media and with the right-hand side only in L^2. The estimator is of the recovery type. Independent with the current approximation to the primary variable (the electric field), an auxiliary variable (the magnetizing field) is recovered in parallel by solving a similar H(curl) problem. An alternate way of recovery is presented as well by localizing the error flux. The estimator is then defined as the sum of the modified element residual and the residual of the constitutive equation defining the auxiliary variable. It is proved that the estimator is approximately equal to the true error in the energy norm without the quasi-monotonicity assumption. Finally, we present numerical results for two H(curl) interface problems.