5 papers · 1 filter
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…
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…
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…
The Lax-Wendroff theorem for Patankar-type methods applied to hyperbolic conservation laws
Janina Bender, Thomas Izgin, Philipp Ãffner +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 Ãffner, 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…