97 citations · 734 across the 50 of their papers we have counts for
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Approximation of the high-frequency Helmholtz kernel by nested directional interpolation
Steffen Börm, Jens Markus Melenk
We present and analyze an approximation scheme for a class of highly oscillatory kernel functions, taking the 2D and 3D Helmholtz kernels as examples. The scheme is based on polyno…
Local inverse estimates for non-local boundary integral operators
Markus Aurada, Michael Feischl, Thomas Führer +3
We prove local inverse-type estimates for the four non-local boundary integral operators associated with the Laplace operator on a bounded d-dimensional Lipschitz domain Omega for…
Existence of -matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator
Markus Faustmann, Jens Markus Melenk, Dirk Praetorius
We consider discretizations of the hyper-singular integral operator on closed surfaces and show that the inverses of the corresponding system matrices can be approximated by blockw…
On optimal - and surface flux convergence in FEM (extended version)
T. Horger, J. M. Melenk, B. Wohlmuth
We show that optimal -convergence in the finite element method on quasi-uniform meshes can be achieved if, for some , the boundary value problem has the mapping pro…