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07/13/2023
A well-balanced discontinuous Galerkin method for the first–order Z4 formulation of the Einstein–Euler system
In this paper we develop a new well-balanced discontinuous Galerkin (DG)...
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06/20/2023
A new thermodynamically compatible finite volume scheme for Lagrangian gas dynamics
The equations of Lagrangian gas dynamics fall into the larger class of o...
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05/17/2023
High-order ADER Discontinuous Galerkin schemes for a symmetric hyperbolic model of compressible barotropic two-fluid flows
This paper presents a high-order discontinuous Galerkin finite element m...
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02/11/2023
An implicit staggered hybrid finite volume/finite element solver for the incompressible Navier-Stokes equations
We present a novel fully implicit hybrid finite volume/finite element me...
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01/23/2023
An Arbitrary-Lagrangian-Eulerian hybrid finite volume/finite element method on moving unstructured meshes for the Navier-Stokes equations
We present a novel second-order semi-implicit hybrid finite volume / fin...
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01/20/2023
A staggered semi-implicit hybrid finite volume / finite element scheme for the shallow water equations at all Froude numbers
We present a novel staggered semi-implicit hybrid FV/FE method for the n...
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01/19/2023
On thermodynamically compatible finite volume schemes for continuum mechanics
In this paper we present a new family of semi-discrete and fully-discret...
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01/19/2023
A semi-implicit hybrid finite volume / finite element scheme for all Mach number flows on staggered unstructured meshes
In this paper a new hybrid semi-implicit finite volume / finite element ...
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01/19/2023
A new thermodynamically compatible finite volume scheme for magnetohydrodynamics
In this paper we propose a novel thermodynamically compatible finite vol...
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05/29/2022
Continuous finite element subgrid basis functions for Discontinuous Galerkin schemes on unstructured polygonal Voronoi meshes
We propose a new high order accurate nodal discontinuous Galerkin (DG) m...
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08/06/2021
A well balanced finite volume scheme for general relativity
In this work we present a novel second order accurate well balanced (WB)...
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12/14/2020
Modeling solid-fluid transformations in non-Newtonian viscoplastic flows with a unified flow theory
We discuss the applicability of a unified hyperbolic model for continuum...
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10/10/2020
A posteriori subcell finite volume limiter for general PNPM schemes: applications from gasdynamics to relativistic magnetohydrodynamics
In this work, we consider the general family of the so called ADER PNPM ...
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09/08/2020
Curl constraint-preserving reconstruction and the guidance it gives for mimetic scheme design
Several important PDE systems, like magnetohydrodynamics and computation...
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05/08/2020
A structure-preserving staggered semi-implicit finite volume scheme for continuum mechanics
We propose a new pressure-based structure-preserving (SP) and quasi asym...
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04/07/2020
High order ADER-DG schemes for the simulation of linear seismic waves induced by nonlinear dispersive free-surface water waves
In this paper, we propose a unified and high order accurate fully-discre...
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03/20/2020
A hyperbolic reformulation of the Serre-Green-Naghdi model for general bottom topographies
We present a novel hyperbolic reformulation of the Serre-Green-Naghdi (S...
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03/15/2020
A novel staggered semi-implicit space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations
A new high order accurate staggered semi-implicit space-time discontinuo...
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03/05/2020
On numerical methods for hyperbolic PDE with curl involutions
In this paper we present three different numerical approaches to account...
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03/05/2020
Space-time adaptive ADER discontinuous Galerkin schemes for nonlinear hyperelasticity with material failure
We are concerned with the numerical solution of a unified first order hy...
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02/20/2020
High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension
In this work, we introduce two novel reformulations of a recent weakly h...
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01/28/2020
A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer-Nunziato model
In this paper we propose a new diffuse interface model for the numerical...
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12/04/2019
High order ADER schemes for continuum mechanics
In this paper we first review the development of high order ADER finite ...
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09/08/2019
On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations
In this paper we propose an extension of the generalized Lagrangian mult...
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05/20/2019
ExaHyPE: An Engine for Parallel Dynamically Adaptive Simulations of Wave Problems
ExaHyPE ("An Exascale Hyperbolic PDE Engine") is a software engine for s...
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10/09/2018