97 citations · 734 across the 50 of their papers we have counts for
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Goal-oriented adaptive finite element method for semilinear elliptic PDEs
Roland Becker, Maximilian Brunner, Michael Innerberger +2
We formulate and analyze a goal-oriented adaptive finite element method (GOAFEM) for a semilinear elliptic PDE and a linear goal functional. The strategy involves the finite elemen…
Weighted analytic regularity for the integral fractional Laplacian in polygons
Markus Faustmann, Carlo Marcati, Jens Markus Melenk +1
We prove weighted analytic regularity of solutions to the Dirichlet problem for the integral fractional Laplacian in polygons with analytic right-hand side. We localize the problem…
-inverses for RBF interpolation
Niklas Angleitner, Markus Faustmann, Jens Markus Melenk
We consider the interpolation problem for a class of radial basis functions (RBFs) that includes the classical polyharmonic splines (PHS). We show that the inverse of the system ma…
Mortar coupling of -discontinuous Galerkin and boundary element methods for the Helmholtz equation
Christoph Erath, Lorenzo Mascotto, Jens Markus Melenk +2
We design and analyze a coupling of a discontinuous Galerkin finite element method with a boundary element method to solve the Helmholtz equation with variable coefficients in thre…
-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equations
Markus Faustmann, Jens Markus Melenk, Maryam Parvizi
The inverse of the stiffness matrix of the time-harmonic Maxwell equation with perfectly conducting boundary conditions is approximated in the blockwise low-rank format of ${\mathc…