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In this article we present a new family of high order accurate ArbitraryLagrangian-Eulerian one-step WENO finite volume schemes for the solution ofstiff hyperbolic balance laws. High order accuracy in space is obtained with astandard WENO reconstruction algorithm and high order in time is obtained usingthe local space-time discontinuous Galerkin method recently proposed inDumbser, Enaux, and Toro (2008). In the Lagrangian framework considered here,the local space-time DG predictor is based on a weak formulation of thegoverning PDE on a moving space-time element. For the space-time basis and testfunctions we use Lagrange interpolation polynomials defined by tensor-productGauss-Legendre quadrature points. The moving space-time elements are mapped toa reference element using an isoparametric approach, i.e. the space-timemapping is defined by the same basis functions as the weak solution of the PDE.We show some computational examples in one space-dimension for non-stiff andfor stiff balance laws, in particular for the Euler equations of compressiblegas dynamics, for the resistive relativistic MHD equations, and for therelativistic radiation hydrodynamics equations. Numerical convergence resultsare presented for the stiff case up to sixth order of accuracy in space andtime and for the non-stiff case up to eighth order of accuracy in space andtime.

On Arbitrary-Lagrangian-Eulerian One-Step WENO Schemes for Stiff Hyperbolic Balance Laws