Artificial viscosity can be combined with a higher-order discontinuous Galerkin (DG) discretization to resolve a shock layer within a single cell. However, when a piecewiseconstant artificial viscosity model is employed with an otherwise higher-order approximation, element-to-element variations in the artificial viscosity arising at the shock induce oscillations in state gradients and pollute t...

The aim of this work is to study of the numerical approximation of the controls for the hinged beam equation. A consequence of the numerical spurious high frequencies is the lack of the uniform controllability property of the semi-discrete model for the beam equation, in the classical setting. We solve this deficiency by adding a vanishing numerical viscosity term, which will damp out these hig...

A new upper bound is provided for the L∞-norm of the difference between the viscosity solution of a model steady state Hamilton-Jacobi equation, u, and any given approximation, v. This upper bound is independent of the method used to compute the approximation v; it depends solely on the values that the residual takes on a subset of the domain which can be easily computed in terms of v. Numerica...

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. We introduce an extragradient-like approximation method which is based on so-called extragradient method and viscosity approximation method. We establish...

We study in this paper the existence and approximation of solutions of variational inequalities involving generalized pseudo-contractive mappings in Banach spaces. The convergence analysis of a proposed hybrid iterative method for approximating common zeros or fixed points of a possibly infinitely countable or uncountable family of such operators will be conducted within the conceptual framewor...

Abstract. We introduce and analyze a spectral vanishing viscosity approximation of periodic fractional conservation laws. The fractional part of these equations can be a fractional Laplacian or other non-local operators that are generators of pure jump Lévy processes. To accommodate for shock solutions, we first extend to the periodic setting the Kružkov-Alibaud entropy formulation and prove we...

We discuss transport properties of dynamical fluid composed of quasi-particles whose masses depend on temperature and charge chemical potentials. Based on the relativistic kinetic theory formulated under the relaxation time approximation, we derive a general expression for the bulk viscosity in the quasi-particle medium. We show that dynamically generated particle masses imply an essential modi...

In this paper, we consider the approximation of second order evolution equations. It is well known that the approximated system by finite element or finite difference is not uniformly exponentially or polynomially stable with respect to the discretization parameter, even if the continuous system has this property. Our goal is to damp the spurious high frequency modes by introducing numerical vi...

We present an analytic description of the r-mode instability in newly-born neutron stars, using the approximation of uniform density. Our computation is consistently accurate to second order in the angular velocity of the star. We obtain formulae for the growth-time of the instability due to gravitationalwave emission, for both current and mass multipole radiation and for the damping timescale,...

We propose a new, black-box online stabilization strategy for reduced basis (RB) approximations of parameter-dependent advection-diffusion problems in the advection-dominated case. Our goal is to stabilize the RB problem irrespectively of the stabilization (if any) operated on the high-fidelity (e.g. finite element) approximation, provided a set of stable RB functions have been computed. Inspir...