67 citations · 166 across the 12 of their papers we have counts for
14 papers
Justification and structure- and asymptotic-preserving discretizations of a hyperbolized Cahn-Hilliard equation
Jan Giesselmann, Fabio Leotta, Hendrik Ranocha +1
We study a hyperbolic approximation ("hyperbolization") of the Cahn-Hilliard (CH) equation, originally proposed by Dhaouadi, Dumbser, and Gavrilyuk (2025, DOI: 10.1098/rspa.2024.06…
Multiderivative time integration methods preserving nonlinear functionals via relaxation
Hendrik Ranocha, Jochen Schütz
We combine the recent relaxation approach with multiderivative Runge-Kutta methods to preserve conservation or dissipation of entropy functionals for ordinary and partial different…
Functional-preserving predictor-corrector multiderivative schemes
Hendrik Ranocha, Jochen Schütz, Eleni Theodosiou
In this work, we develop a class of high-order multiderivative time integration methods that is able to preserve certain functionals discretely. Important ingredients are the recen…
Two-derivative deferred correction time discretization for the discontinuous Galerkin method
Jonas Zeifang, Jochen Schuetz
In this paper, we use an implicit two-derivative deferred correction time discretization approach and combine it with a spatial discretization of the discontinuous Galerkin spectra…
Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations
Václav Kučera, Mária Lukáčová-Medvid'ová, Sebastian Noelle +1
In this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Kučera (JCP 2007) as well as the class of RS-IMEX schemes. The impl…
FESTUNG: A MATLAB / GNU Octave toolbox for the discontinuous Galerkin method. Part III: Hybridized discontinuous Galerkin (HDG) formulation
Alexander Jaust, Balthasar Reuter, Vadym Aizinger +2
The third paper in our series on open source MATLAB / GNU Octave implementation of the discontinuous Galerkin (DG) method(s) focuses on a hybridized formulation. The main aim of th…
Implicit multiderivative collocation solvers for linear partial differential equations with discontinuous Galerkin spatial discretizations
Jochen Schütz, David C. Seal, Alexander Jaust
In this work, we construct novel discretizations for the unsteady convection-diffusion equation. Our discretization relies on multiderivative time integrators together with a novel…
Implicit multistage two-derivative discontinuous Galerkin schemes for viscous conservation laws
Alexander Jaust, Jochen Schütz, David C. Seal
In this paper we apply implicit two-derivative multistage time integrators to viscous conservation laws in one and two dimensions. The one dimensional solver discretizes space with…
Flux Splitting for stiff equations: A notion on stability
Jochen Schütz, Sebastian Noelle
For low Mach number flows, there is a strong recent interest in the development and analysis of IMEX (implicit/explicit) schemes, which rely on a splitting of the convective flux i…
A note on adjoint error estimation for one-dimensional stationary balance laws with shocks
Jochen Schütz, Sebastian Noelle, Christina Steiner +1
We consider one-dimensional steady-state balance laws with discontinuous solutions. Giles and Pierce realized that a shock leads to a new term in the adjoint error representation f…
An asymptotic preserving method for linear systems of balance laws based on Galerkin's method
Jochen Schütz
We apply the concept of Asymptotic Preserving (AP) schemes to the linearized p-system and discretize the resulting elliptic equation using standard continuous Finite Elements inste…
A temporally adaptive hybridized discontinuous Galerkin method for time-dependent compressible flows
Alexander Jaust, Jochen Schütz
The potential of the hybridized discontinuous Galerkin (HDG) method has been recognized for the computation of stationary flows. Extending the method to time-dependent problems can…
Adjoint-Based Error Estimation and Mesh Adaptation for Hybridized Discontinuous Galerkin Methods
Michael Woopen, Georg May, Jochen Schütz
We present a robust and efficient target-based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection-diffusion problems, inc…
A Comparison of Hybridized and Standard DG Methods for Target-Based hp-Adaptive Simulation of Compressible Flow
Michael Woopen, Aravind Balan, Georg May +1
We present a comparison between hybridized and non-hybridized discontinuous Galerkin methods in the context of target-based hp-adaptation for compressible flow problems. The aim is…