17 citations · 62 across the 22 of their papers we have counts for
21 papers · 1 filter
Towards provable energy-stable overset grid methods using sub-cell summation-by-parts operators
Jan Glaubitz, Joshua Lampert, Andrew R. Winters +1
Overset grid methods handle complex geometries by overlapping simpler, geometry-fitted grids to cover the original, more complex domain. However, ensuring their stability---particu…
Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators
Wasilij Barsukow, Christian Klingenberg, Lisa Lechner +3
The Active Flux method is a numerical method for conservation laws using a combination of cell averages and point values as independent degrees of freedom, based on ideas from fini…
Global Bounds for the Error in Solutions of Linear Hyperbolic Systems due to Inaccurate Boundary Geometry
David A. Kopriva, Andrew R. Winters, Jan Nordström
Meshes approximate the boundaries of a geometry when the boundaries are curved. The accuracy of the mesh then affects the error of computations of initial boundary value problems f…
An optimization-based construction procedure for function space based summation-by-parts operators on arbitrary grids
Jan Glaubitz, Jan Nordström, Philipp Öffner
We introduce a novel construction procedure for one-dimensional summation-by-parts (SBP) operators. Existing construction procedures for FSBP operators of the form p…
Energy Bounds for Discontinuous Galerkin Spectral Element Approximations of Well-Posed Overset Grid Problems for Hyperbolic Systems
David A. Kopriva, Andrew R. Winters, Jan Nordström
We show that even though the Discontinuous Galerkin Spectral Element Method is stable for hyperbolic boundary-value problems, and the overset domain problem is well-posed in an app…
Exact symmetry conservation and automatic mesh refinement in discrete initial boundary value problems
Alexander Rothkopf, W. A. Horowitz, Jan Nordström
We present a novel solution procedure for initial boundary value problems. The procedure is based on an action principle, in which coordinate maps are included as dynamical degrees…