Alexei Bespalov

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We consider Dirichlet boundary value problems for second order elliptic equations over polygonal domains. The coefficients of the equations under consideration degenerate at an inner point of the domain, or behave singularly in the neighborhood of that point. This behavior may cause singu-larities in the solution. The solvability of the problems is proved(More)
We consider the variational formulation of the electric field integral equation (EFIE) on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based on div Γ-conforming Raviart-Thomas boundary elements (BEM) of locally variable polynomial degree on shape-regular surface meshes. We establish asymptotic quasi-optimality(More)
In this paper we prove an optimal error estimate for the H(curl)-conforming projection based p-interpolation operator introduced in [L. Demkowicz and I. Babuška, p interpolation error estimates for edge finite elements of variable order in two dimensions, SIAM J. Numer. This result is proved on the reference element (either triangle or square) K for regular(More)