Invariant domains preserving ALE approximation of hyperbolic systems   with continuous finite elements
  A conservative invariant domain preserving Arbitrary Lagrangian Eulerian method for solving nonlinear hyperbolic systems is introduced. The method is explicit in time, works with continuous finite elements and is first-order accurate in space. One originality of the present work is that the artificial viscosity is unambiguously defined irrespective of the mesh geometry/anisotropy and does not depend on any ad hoc parameter. The proposed method is meant to be a stepping stone for the construction of higher-order methods in space by using appropriate limitation techniques. 
Jean-Luc Guermond and Bojan and Laura Saavedra and Yong Yang
math.NA