46 citations · 230 across the 16 of their papers we have counts for
18 papers
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…
New Efficient Implicit-Explicit Deferred Correction methods
Lorenzo Micalizzi, Davide Torlo
In this work, we investigate implicit-explicit (IMEX) arbitrary high-order Deferred Correction (DeC) methods for the approximation of ordinary differential equations (ODEs). Such s…
Flux-Balanced Patankar-type Schemes for the Compressible Euler Equations
Thomas Izgin, Andreas Meister, Chi-Wang Shu +1
Positivity preservation of key physical quantities in the context of fluid flows, such as density and internal energy, is an essential property of a numerical scheme as otherwise t…
Stability analysis of Arbitrary-Lagrangian-Eulerian ADER-DG methods on classical and degenerate spacetime geometries
Mauro Bonafini, Davide Torlo, Elena Gaburro
In this paper, we present a thorough von Neumann stability analysis of explicit and implicit Arbitrary-Lagrangian-Eulerian (ALE) ADER discontinuous Galerkin (DG) methods on classic…
The Lax-Wendroff theorem for Patankar-type methods applied to hyperbolic conservation laws
Janina Bender, Thomas Izgin, Philipp Öffner +1
For hyperbolic conservation laws, the famous Lax-Wendroff theorem delivers sufficient conditions for the limit of a convergent numerical method to be a weak (entropy) solution. Thi…
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 improving the efficiency of ADER methods
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
The (modern) arbitrary derivative (ADER) approach is a popular technique for the numerical solution of differential problems based on iteratively solving an implicit discretization…
Efficient iterative arbitrary high order methods: an adaptive bridge between low and high order
Lorenzo Micalizzi, Davide Torlo, Walter Boscheri
We propose a new paradigm for designing efficient p-adaptive arbitrary high order methods. We consider arbitrary high order iterative schemes that gain one order of accuracy at eac…
A necessary condition for non oscillatory and positivity preserving time-integration schemes
Thomas Izgin, Philipp Öffner, Davide Torlo
Modified Patankar (MP) schemes are conservative, linear implicit and unconditionally positivity preserving time-integration schemes constructed for production-destruction systems.…
A new efficient explicit Deferred Correction framework: analysis and applications to hyperbolic PDEs and adaptivity
Lorenzo Micalizzi, Davide Torlo
The Deferred Correction (DeC) is an iterative procedure, characterized by increasing accuracy at each iteration, which can be used to design numerical methods for systems of ODEs.…
Spectral analysis of high order continuous FEM for hyperbolic PDEs on triangular meshes: influence of approximation, stabilization, and time-stepping
Sixtine Michel, Davide Torlo, Mario Ricchiuto +1
In this work we study various continuous finite element discretization for two dimensional hyperbolic partial differential equations, varying the polynomial space (Lagrangian on eq…
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…
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…
Arbitrary high-order, conservative and positive preserving Patankar-type deferred correction schemes
Philipp Öffner, Davide Torlo
Production-destruction systems (PDS) of ordinary differential equations (ODEs) are used to describe physical and biological reactions in nature. The considered quantities are subje…