Clemens Hofreither

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Recently, C. Hofreither, U. Langer and C. Pechstein have analyzed a nonstandard finite element method based on element-local boundary integral operators. The method is able to treat general polyhedral meshes and employs locally PDE-harmonic trial functions. In the previous work, the primal formulation of the method has been analyzed as a perturbed Galerkin(More)
In this article, we provide a rigorous a priori error estimate for the symmetric coupling of the finite and boundary element method for the potential problem in three dimensions. Our theoretical framework allows an arbitrary number of poly-hedral subdomains. Our bound is not only explicit in the mesh parameter, but also in the subdomains themselves: the(More)
We construct a class of cubature formulae for harmonic functions on the unit disk based on line integrals over 2n + 1 distinct chords. These chords are assumed to have constant distance t to the center of the disk, and their angles to be equispaced over the interval [0, 2π]. If t is chosen properly, these formulae integrate exactly all harmonic polynomials(More)
Given information about a harmonic function in two variables, consisting of a nite number of values of its Radon projections, i.e., integrals along some chords of the unit circle, we study the problem of interpolating these data by a harmonic polynomial. With the help of symbolic summation techniques we show that this interpolation problem has a unique(More)
We investigate geometric multigrid methods for solving the large, sparse linear systems which arise in isogeometric discretizations of elliptic partial differential equations. We observe that the performance of standard V-cycle iteration is highly dependent on the spatial dimension as well as the spline degree of the discretization space. Conjugate gradient(More)