Arbitrary Lagrangian-Eulerian Finite Element Method Preserving Convex Invariants of Hyperbolic Systems

  • Jean-Luc GuermondEmail author
  • Bojan Popov
  • Laura Saavedra
  • Yong Yang
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 47)


We present a conservative Arbitrary Lagrangian Eulerian method for solving nonlinear hyperbolic systems. The key characteristics of the method is that it preserves all the convex invariants of the hyperbolic system in question. The method is explicit in time, uses continuous finite elements and is first-order accurate in space and high-order in time. The stability of the method is obtained by introducing an artificial viscosity that is unambiguously defined irrespective of the mesh geometry/anisotropy and does not depend on any ad hoc parameter.


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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Jean-Luc Guermond
    • 1
    Email author
  • Bojan Popov
    • 1
  • Laura Saavedra
    • 2
  • Yong Yang
    • 3
  1. 1.Department of MathematicsTexas A&M University 3368 TAMUCollege StationUSA
  2. 2.Departamento Fundamentos Matemáticos, Departamento de Matematica Aplicada a la Ingenieria AeroespacialUniversidad Politécnica de MadridMadridSpain
  3. 3.Department of MathematicsPenn State UniversityState CollegeUSA

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