INVARIANT DOMAINS PRESERVING ARBITRARY LAGRANGIAN EULERIAN APPROXIMATION OF HYPERBOLIC SYSTEMS WITH CONTINUOUS FINITE ELEMENTS
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2017 Societ y for Industrial and Applied Mathematics. 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 original element 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.