76 citations · 1.5k across the 82 of their papers we have counts for
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Optimal preconditioning for the symmetric and non-symmetric coupling of adaptive finite elements and boundary elements
Michael Feischl, Thomas Führer, Dirk Praetorius +1
We analyze a multilevel diagonal additive Schwarz preconditioner for the adaptive coupling of FEM and BEM for a linear 2D Laplace transmission problem. We rigorously prove that the…
Existence of -matrix approximants to the inverses of BEM matrices: the simple-layer operator
Markus Faustmann, Jens Markus Melenk, Dirk Praetorius
We consider the question of approximating the inverse of the Galerkin stiffness matrix obtained by discretizing the simple-layer operator $…
Efficient additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations
Michael Feischl, Thomas Führer, Dirk Praetorius +1
For non-preconditioned Galerkin systems, the condition number grows with the number of elements as well as the quotient of the maximal and the minimal mesh-size. Therefore, reliabl…
H-matrix approximability of the inverses of FEM matrices
Markus Faustmann, Jens Markus Melenk, Dirk Praetorius
We study the question of approximability for the inverse of the FEM stiffness matrix for (scalar) second order elliptic boundary value problems by blockwise low rank matrices such…
L2-orthogonal projections onto finite elements on locally refined meshes are H1-stable
Michael Karkulik, Carl-Martin Pfeiler, Dirk Praetorius
We merge and extend recent results which prove the H1-stability of the L2-orthogonal projection onto standard finite element spaces, provided that the underlying simplicial triangu…
ZZ-type aposteriori error estimators for adaptive boundary element methods on a curve
Michael Feischl, Thomas Führer, Michael Karkulik +1
In the context of the adaptive finite element method (FEM), ZZ-error estimators named after Zienkiewicz and Zhu are mathematically well-established and widely used in practice. In…