118 citations · 565 across the 34 of their papers we have counts for
36 papers · 1 filter
High-order positivity-preserving well-balanced schemes: combining flux globalization with modified Patankar deferred correction methods
Philipp Öffner, Michael Redle, Davide Torlo
Positivity-preserving schemes for hyperbolic balance laws are typically built from the Zhang-Shu limiter and strong-stability-preserving Runge-Kutta (SSP-RK) time stepping, at the…
Entropy dissipative high order schemes for a hyperbolic model of two-layer thin film flow
Rahul Barthwal, Philipp Öffner, Chetan Singh +1
In this article, we develop high-order, entropy-dissipative schemes for a hyperbolic system of conservation laws describing the first-order dynamics of two-layer thin-film flows of…
Gaussian FSBP operators: Comparison and application to numerical methods for hyperbolic conservation laws
Jan Glaubitz, Henry Haase, Philipp Öffner +1
Function-space summation-by-parts (FSBP) operators enable conservative and energy-stable numerical methods for hyperbolic conservation laws based on general, non-polynomial approxi…
Convergence analysis of structure-preserving schemes for the multicomponent compressible Euler flows
Jaya Agnihotri, Philipp Öffner
We present a convergence analysis of a finite volume (FV) scheme for the multicomponent compressible Euler system in the framework of dissipative weak (DW) solutions. DW solutions…
A high-order, structure preserving scheme for the stochastic Galerkin shallow water equations -- unification and two-dimensional extension
Philipp Öffner, Per Pettersson, Andrew R. Winters
Recently, two independent research efforts have been made to study the stochastic Galerkin formulation of the shallow water equations. Bender and Öffner developed entropy-conservat…
Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods
Jan Glaubitz, Hendrik Ranocha, Andrew R. Winters +3
High-order numerical methods for conservation laws are highly sought after due to their potential efficiency. However, it is challenging to ensure their robustness, particularly fo…
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…
Analysis for Implicit and Implicit-Explicit ADER and DeC Methods for Ordinary Differential Equations, Advection-Diffusion and Advection-Dispersion Equations
Philipp Öffner, Louis Petri, Davide Torlo
In this manuscript, we present the development of implicit and implicit-explicit ADER and DeC methodologies within the DeC framework using the two-operators formulation, with a foc…
A high-order, fully well-balanced, unconditionally positivity-preserving finite volume framework for flood simulations
Mirco Ciallella, Lorenzo Micalizzi, Victor Michel-Dansac +2
In this work, we present a high-order finite volume framework for the numerical simulation of shallow water flows. The method is designed to accurately capture complex dynamics inh…
On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws
Hendrik Ranocha, Andrew R. Winters, Michael Schlottke-Lakemper +3
We use the framework of upwind summation-by-parts (SBP) operators developed by Mattsson (2017, doi:10.1016/j.jcp.2017.01.042) and study different flux vector splittings in this con…
Consistency and convergence of flux-corrected finite element methods for nonlinear hyperbolic problems
Dmitri Kuzmin, Mária Lukácova-Medvid'ová, Philipp Öffner
We investigate the consistency and convergence of flux-corrected finite element approximations in the context of nonlinear hyperbolic conservation laws. In particular, we focus on…
Summation-by-parts operators for general function spaces: The second derivative
Jan Glaubitz, Simon-Christian Klein, Jan Nordström +1
Many applications rely on solving time-dependent partial differential equations (PDEs) that include second derivatives. Summation-by-parts (SBP) operators are crucial for developin…
Multi-dimensional summation-by-parts operators for general function spaces: Theory and construction
Jan Glaubitz, Simon-Christian Klein, Jan Nordström +1
Summation-by-parts (SBP) operators allow us to systematically develop energy-stable and high-order accurate numerical methods for time-dependent differential equations. Until recen…
Fully well-balanced entropy controlled discontinuous Galerkin spectral element method for shallow water flows: global flux quadrature and cell entropy correction
Yogiraj Mantri, Philipp Öffner, Mario Ricchiuto
We present a novel approach for solving the shallow water equations using a discontinuous Galerkin spectral element method. The method we propose has three main features. First, it…
A new variable shape parameter strategy for RBF approximation using neural networks
Fatemeh Nassajian Mojarrad, Maria Han Veiga, Jan S. Hesthaven +1
The choice of the shape parameter highly effects the behaviour of radial basis function (RBF) approximations, as it needs to be selected to balance between ill-condition of the int…
On the convergence of residual distribution schemes for the compressible Euler equations via dissipative weak solutions
Rémi Abgrall, Mária Lukácova-Medvid'ová, Philipp Öffner
In this work, we prove the convergence of residual distribution schemes to dissipative weak solutions of the Euler equations. We need to guarantee that the residual distribution sc…
High order entropy preserving ADER scheme
Elena Gaburro, Philipp Öffner, Mario Ricchiuto +1
In this paper, we develop a fully discrete entropy preserving ADER-Discontinuous Galerkin (ADER-DG) method. To obtain this desired result, we equip the space part of the method wit…
A study of the local dynamics of modified Patankar DeC and higher order modified Patankar RK methods
Thomas Izgin, Philipp Öffner
Patankar schemes have attracted increasing interest in recent years because they preserve the positivity of the analytical solution of a production-destruction system (PDS) irrespe…
Summation-by-parts operators for general function spaces
Jan Glaubitz, Jan Nordström, Philipp Öffner
Summation-by-parts (SBP) operators are popular building blocks for systematically developing stable and high-order accurate numerical methods for time-dependent differential equati…
An Arbitrary High Order and Positivity Preserving Method for the Shallow Water Equations
Mirco Ciallella, Lorenzo Micalizzi, Philipp Öffner +1
In this paper, we develop and present an arbitrary high order well-balanced finite volume WENO method combined with the modified Patankar Deferred Correction (mPDeC) time integrati…
Issues with Positivity-Preserving Patankar-type Schemes
Davide Torlo, Philipp Öffner, Hendrik Ranocha
Patankar-type schemes are linearly implicit time integration methods designed to be unconditionally positivity-preserving. However, there are only little results on their stability…
Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes
Rémi Abgrall, Elise Le Mélédo, Philipp Öffner +1
In [1] is proposed a simplified DeC method, that, when combined with the residual distribution (RD) framework, allows to construct a high order, explicit FE scheme with continuous…
DeC and ADER: Similarities, Differences and a Unified Framework
Maria Han Veiga, Philipp Öffner, Davide Torlo
In this paper, we demonstrate that the explicit ADER approach as it is used inter alia in [1] can be seen as a special interpretation of the deferred correction (DeC) method as int…
Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes: Application to Structure Preserving Discretization
Rémi Abgrall, Philipp Öffner, Hendrik Ranocha
For the general class of residual distribution (RD) schemes, including many finite element (such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach…