The general setting that we will discuss, can be written as follows: Mu = f. Here M : X → Y is some given operator for ordered spaces X,Y . The question for this generic equation is: Can one classify M for which it holds that f ≥ 0 =⇒ u ≥ 0? In other words, when do we a have a positivity preserving property in the sense that a positive source gives a positive solution. • Our main focus is on pa...

This paper presents a class of novel high-order accurate discontinuous Galerkin (DG) schemes for the compressible Euler equations under gravitational fields. A notable feature these is that they are well-balanced general hydrostatic equilibrium state, and at same time, provably preserve positivity density pressure. In order to achieve positivity-preserving properties simultaneously, DG spatial ...

Abstract This paper contributes new insights into discretizing Coulomb collisions in kinetic plasma models. Building on the previous works (Carrillo et al 2020 J. Comput. Phys. X 7 100066; Hirvijoki and Burby Plasmas 27 082307), I propose deterministic discrete-time energy- positivity-preserving, entropy-dissipating marker-particle schemes for standard Landau collision operator electrostatic gy...

We consider a class of finite element approximations for fourth-order parabolic equations that can be written as system second-order by introducing an auxiliary variable. In our approach, we first solve variational problem and then optimization to satisfy the desired physical properties solution such conservation mass, positivity (non-negativity) dissipation energy. Furthermore, show existence ...