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A conservative invariant domain preserving Arbitrary Lagrangian Eulerianmethod for solving nonlinear hyperbolic systems is introduced. The method isexplicit in time, works with continuous finite elements and is first-orderaccurate in space. One originality of the present work is that the artificialviscosity is unambiguously defined irrespective of the mesh geometry/anisotropyand does not depend on any ad hoc parameter. The proposed method is meant to bea stepping stone for the construction of higher-order methods in space by usingappropriate limitation techniques.

Invariant domains preserving ALE approximation of hyperbolic systems with continuous finite elements