Entropy solutions have been widely accepted as the suitable solution framework for systems
of conservation laws in several space dimensions. However, recent results in De Lellis and …

We extend the multi-level Monte Carlo (MLMC) in order to quantify uncertainty in the
solutions of multi-dimensional hyperbolic systems of conservation laws with uncertain initial …

We present a highly robust second order accurate scheme for the Euler equations and the
ideal MHD equations. The scheme is of predictor–corrector type, with a MUSCL scheme …

We review uncertainty quantification (UQ) for hyperbolic systems of conservation (balance)
laws. The input uncertainty could be in the initial data, fluxes, coefficients, source terms or …

We study systems of partial differential-algebraic equations (PDAEs) of first order. Classical
solutions of the theory of hyperbolic partial differential equation such as discontinuities …

An E-CUSP (energy-convective upwind and split pressure) scheme is developed to solve
the equations of magnetohydrodynamics. Fifth order WENO reconstructions are employed to …

A mathematical formulation of conservation and of balance laws with random input data,
specifically with random initial conditions, random source terms and random flux functions, is …

Wave propagation in idealized stellar atmospheres is modeled by the equations of ideal
MHD, together with the gravity source term. The waves are modeled as small perturbations …

Abstract The Multi-Level Monte Carlo finite volumes (MLMC-FVM) algorithm was shown to
be a robust and fast solver for uncertainty quantification in the solutions of multi-dimensional …

A mathematical formulation of conservation and of balance laws with random input data is
reviewed, specifically with random initial conditions, source terms, flux functions and …