Clemens Hofreither

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We present and analyze a non-standard finite element method based on element-local boundary integral operators that permits polyhedral element shapes as well as meshes with hanging nodes. The method employs elementwise PDE-harmonic trial functions and can thus be interpreted as a local Trefftz method. The construction principle requires the explicit(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 present efficient domain decomposition solvers for a class of non-standard finite element methods (FEM). These methods utilize PDE-harmonic trial functions in every element of a polyhedral mesh, and use boundary element techniques locally in order to assemble the finite element stiffness matrices. For these reasons, the terms BEM-based FEM or Trefftz-FEM(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)
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)
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)