40 citations · 89 across the 11 of their papers we have counts for
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Convergence analysis of some tent-based schemes for linear hyperbolic systems
Dow Drake, Jay Gopalakrishnan, Joachim Schöberl +1
Finite element methods for symmetric linear hyperbolic systems using unstructured advancing fronts (satisfying a causality condition) are considered in this work. Convergence resul…
Structure aware Runge-Kutta time stepping for spacetime tents
Jay Gopalakrishnan, Joachim Schöberl, Christoph Wintersteiger
We introduce a new class of Runge-Kutta type methods suitable for time stepping to propagate hyperbolic solutions within tent-shaped spacetime regions. Unlike standard Runge-Kutta…
Tent pitching and Trefftz-DG method for the acoustic wave equation
Ilaria Perugia, Joachim Schöberl, Paul Stocker +1
We present a space-time Trefftz discontinuous Galerkin method for approximating the acoustic wave equation semi-explicitly on tent pitched meshes. DG Trefftz methods use discontinu…
An Explicit Mapped Tent Pitching Scheme for Maxwell Equations
Jay Gopalakrishnan, Matthias Hochsteger, Joachim Schöberl +1
We present a new numerical method for solving time dependent Maxwell equations, which is also suitable for general linear hyperbolic equations. It is based on an unstructured parti…
Higher order unfitted FEM for Stokes interface problems
Philip Lederer, Carl-Martin Pfeiler, Christoph Wintersteiger +1
We consider the discretization of a stationary Stokes interface problem in a velocity-pressure formulation. The interface is described implicitly as the zero level of a scalar func…
Mapped tent pitching schemes for hyperbolic systems
J. Gopalakrishnan, J. Schöberl, C. Wintersteiger
A spacetime domain can be progressively meshed by tent shaped objects. Numerical methods for solving hyperbolic systems using such tent meshes to advance in time have been proposed…