As the total value of the global financial market outgrew the value of the real economy,
financial institutions created a global web of interactions that embodies systemic risks …

High order methods based on diagonal-norm summation by parts operators can be shown
to satisfy a discrete conservation or dissipation of entropy for nonlinear systems of …

In this paper, we present a new limiter for discontinuous Galerkin (DG) schemes, based on
subcell resolution through reconstructed flux correction, for hyperbolic conservation laws …

We are interested in the approximation of a steady hyperbolic problem. In some cases, the
solution can satisfy an additional conservation relation, at least when it is smooth. This is the …

Recently, it was discovered that the entropy-conserving/dissipative high-order split-form
discontinuous Galerkin discretizations have robustness issues when trying to solve the …

We present a novel formulation of the discontinuous Galerkin spectral element method for
solving balance laws, with application to the shallow water equations. The scheme …

Production-destruction systems (PDS) of ordinary differential equations (ODEs) are used to
describe physical and biological reactions in nature. The considered quantities are subject …

In the hyperbolic research community, there exists the strong belief that a continuous
Galerkin scheme is notoriously unstable and additional stabilization terms have to be added …

In the hyperbolic community, discontinuous Galerkin (DG) approaches are mainly applied
when finite element methods are considered. As the name suggested, the DG framework …

Many modern discontinuous Galerkin (DG) methods for conservation laws make use of
summation by parts operators and flux differencing to achieve kinetic energy preservation or …