A POSTERIORI ERROR ESTIMATES FOR MAXWELL EQUATIONS

Abstract. Maxwell equations are posed as variational boundary value problems in the function space H(curl) and are discretized by Nédélec finite elements. In [4], 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 introduced recently in [22]. Similar estimates are required for additive Schwarz preconditioning. To incorporate boundary conditions, we establish a new extension result. 1