Abstract
In this paper, we propose, analyze, and numerically validate an adaptive finite element method for two-dimensional time-harmonic magnetic induction intensity equations as well as their Perfectly Matched-Layer (PML) equations. Based on Hodge decomposition, the equations are transformed into scalar elliptic boundary value problems and numerically solved by using the P1 finite element method. Also, we can solve another basic quantity E concerned in physics. A posterior error indicator based on a superconvergent functional value recovery is considered for the two kinds of equations. Numerical experiments are presented to illustrate the effectiveness of the a posterior error indicator and the corresponding adaptive algorithm.
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