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In this paper, we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell’s equations. We present the preconditioners for the first family and second family of higher order Nédélec element equations, respectively. By combining the stable decompositions of two kinds of edge finite element spaces with the abstract theory of auxiliary space preconditioning,...
In this paper, we discuss the error estimation of the linear finite element solution on criss-cross mesh. Using space orthogonal decomposition techniques, we obtain an asymptotic expansion and superconvergence results of the finite element solution. We first prove that the asymptotic expansion has different forms on the two kinds of nodes and then derive a high accuracy combination formula of the...
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