97 citations · 734 across the 50 of their papers we have counts for
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Stable decompositions of -BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D
Michael Karkulik, Jens Markus Melenk, Alexander Rieder
We consider fractional Sobolev spaces , , on a 2D surface . We show that functions in can be decomposed into contributions with local support in a s…
-matrix approximability of inverses of discretizations of the fractional Laplacian
Michael Karkulik, Jens Markus Melenk
The integral version of the fractional Laplacian on a bounded domain is discretized by a Galerkin approximation based on piecewise linear functions on a quasi-uniform mesh. We show…
Analysis of the -version of a first order system least squares method for the Helmholtz equation
Maximilian Bernkopf, Jens Markus Melenk
Extending the wavenumber-explicit analysis of [Chen & Qiu, J. Comput. Appl. Math. 309 (2017)], we analyze the -convergence of a least squares method for the Helmholtz equation…
Wavenumber-explicit -FEM analysis for Maxwell's equations with transparent boundary conditions
Jens Markus Melenk, Stefan Sauter
The time-harmonic Maxwell equations at high wavenumber are discretized by edge elements of degree on a mesh of width . For the case of a ball and exact, transparent boun…
On commuting -version projection-based interpolation on tetrahedra
Jens Markus Melenk, Claudio Rojik
On the reference tetrahedron , we define three projection-based interpolation operators on , ,…