We introduce a simple and general framework for the construction of thermodynamically
compatible schemes for the numerical solution of overdetermined hyperbolic PDE systems …

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 …

We present a new exactly divergence-free and well-balanced hybrid finite volume/finite
element scheme for the numerical solution of the incompressible viscous and resistive …

In this paper, we present a pressure-based semi-implicit numerical scheme for a first order
hyperbolic formulation of compressible two-phase flow with surface tension and viscosity …

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 each …

We present a quantitative assessment of the impact of high-order map**s on the
simulation of flows over complex orography. Curved boundaries were not used in early …

The (modern) arbitrary derivative (ADER) approach is a popular technique for the numerical
solution of differential problems based on iteratively solving an implicit discretization of their …

We develop a novel and efficient discontinuous Galerkin spectral element method (DG-
SEM) for the spherical rotating shallow water equations in vector invariant form. We prove …

The space–time adaptive ADER–DG finite element method with LST–DG predictor and a
posteriori sub–cell ADER–WENO finite–volume limiting was used for simulation of …

In this work we propose a simple but effective high order polynomial correction allowing to
enhance the consistency of all kind of boundary conditions for the Euler equations (Dirichlet …