“...We construct uniformly high order accurate discontinuous Galerkin (DG) schemes which preserve positivity of density and pressure for Euler equations of...”

“...A front tracking scheme for the ultra-relativistic Euler equations is introduced. This scheme is based on piecewise constant approximations to the front...”

“...In Zhang and Shu (2010) [20], Zhang and Shu (2011) [21] and Zhang et al. (in press) [23], we constructed uniformly high order accurate discontinuous Galerkin...”

“...The flux-approximation problem of the relativistic Euler equations for polytropic gas in special relativity is studied. At first, we solve the Riemann problem...”

“...•Truly multi-dimensional.•All-speed schemes.•For the Euler equations on Cartesian grids. Finite volume schemes often have difficulties to resolve the low Mach...”

“...For the free probability analogue of Euclidean space endowed with the Gaussian measure we apply the approach of Arnold to derive Euler equations for a Lie...”

“...Can every measure-valued solution to the compressible Euler equations be approximated by a sequence of weak solutions? We prove that the answer is negative:...”

“...A Hermite WENO reconstruction-based discontinuous Galerkin method RDG(P1P2), designed not only to enhance the accuracy of discontinuous Galerkin method but...”

“...We construct global weak solutions of the Euler equations in an infinite cylinder Π={x∈R3|xh=(x1,x2),r=|xh|<1} for axisymmetric initial data without swirl when...”

“...Here, we have analyzed the weights of the fifth-order finite difference weighted essentially non-oscillatory WENO-P scheme developed by Kim et al. (J. Sci...”