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)
The fast solution of linear systems arising from an isogeometric dis-cretization of a partial differential equation is of great importance for the practical use of Isogeometric Analysis. For classical finite element discretizations, multigrid methods are well known to be fast solvers showing optimal convergence behavior. However, if a geometric multigrid(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)
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)
The dynamics of beams that undergo large displacements is analyzed in frequency domain and comparisons between models derived by isogeometric analysis and p-FEM are presented. The equation of motion is derived by the principle of virtual work, assuming Timoshenko's theory for bending and geometrical type of nonlinearity. As a result, a nonlinear system of(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)