arXiv subjects

Norbert Heuer

Publications and source records attributed to Norbert Heuer.

57 records · Page 4Linked to original sources

arXiv2009

Optimal error estimation for H(curl)-conforming p-interpolation in two dimensions

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. Babuska, p interpolation error estimates for edge finite elements of variable order in two dimensions, SIAM J. Numer. Anal., 41 (2003), pp. 1195-1208]. This result is proved on the reference element (either triangle or square) K for regular vector fields in H^r(curl,K) with arbitrary r>0. The formulation of the result in the H(div)-conforming setting, which is relevant for the analysis of high-order boundary element approximations for Maxwell's equations, is provided as well.

math.NA↗

arXiv2009

Mortar Boundary Elements

We establish a mortar boundary element scheme for hypersingular boundary integral equations representing elliptic boundary value problems in three dimensions. We prove almost quasi-optimal convergence of the scheme in broken Sobolev norms of order 1/2. Sub-domain decompositions can be geometrically non-conforming and meshes must be quasi-uniform only on sub-domains. Numerical results confirm the theory.

math.NA↗

arXiv2008

On the convergence of the hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces

In this paper the hp-version of the boundary element method is applied to the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. The underlying meshes are supposed to be quasi-uniform. We use H(div)-conforming discretisations with quadrilateral elements of Raviart-Thomas type and establish quasi-optimal convergence of hp-approximations. Main ingredient of our analysis is a new H^{-1/2}(div)-conforming p-interpolation operator that assumes only H^r \cap H^{-1/2}(div)-regularity (r > 0) and for which we show quasi-stability with respect to polynomial degrees.

math.NA↗