Abstract A Lagrange finite element method is proposed for Maxwell’s equations in Lipschitz domains. The suitable the approximation of singular solutions lying outside $(H^1(\varOmega ))^3$, with nonhomogeneous boundary data tangential trace space $H({\mathbf{curl}}; \varOmega )$ and a right-hand-side source term $(H_0({\mathbf{curl}}; ))^{\prime}$ (the dual $H_0({\mathbf{curl}}; ))$. Numerical ...

In this article the new method for the accounting singular point influence to the postprocessing error estimation is proposed. Solution improvement in singular zones is achieved modifying physical coordinate matrix used in least square problem equations: instead of the standard quadratic polynomial a new polynomial with singular elements is taken. Numerical examples demonstrate the advantages o...

The classification of polarization elements, the polarization affecting optical devices which have a Jones-matrix representation, according to the type of eigenvectors they possess, is given a new visit through the Group-Theoretical connection of polarization elements. The diattenuators and retarders are recognized as the elements corresponding to boosts and rotations, respectively. The structu...

 The accuracy of finite element approximation on tetrahedral elements is studied using the previously derived maximum eigenvalue condition. This condition is linked with the minimum singular value of the element ‘edge shape matrix’ that characterizes the flatness of an element. A geometric interpretation of these results is discussed. From the theoretical viewpoint, a better insight into the m...

DIAGONAL ELEMENTS, EIGENVALUES, AND SINGULAR VALUES DRAFT AS OF April 30, 2013 SHENG-JHIH WU AND MOODY T. CHU Abstract. Diagonal entries and eigenvalues of a Hermitian matrix, diagonal entries and singular values of a general matrix, and eigenvalues and singular values of a general matrix satisfy necessarily some majorization relationships which turn out also to be sufficient conditions. The in...