COMPLAS 2023

A C1 -Conforming Arbitrary-Order Two-Dimensional Virtual Element Method for the Fourth-Order Phase-field Equation

  • Manzini, Gianmarco (Los Alamos National Laboratory)
  • Adak, Dibyendu (GIMNAP)
  • Mourad, Hashem (Los Alamos National Laboratory)
  • Plohr, JeeYon (Los Alamos National Laboratory)
  • Svolos, Lampros (Los Alamos National Laboratory)

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We present a conforming virtual element method for the two-dimensional High-Order Phase Field (HOPF) equation [2]. This equation is a fourth-order equation and our numerical approximation relies on the design of an arbitrary order accurate, virtual element space with C1 global regularity. Such regularity is guaranteed by taking the values of the virtual element functions and their full gradient at the mesh vertices as degrees of freedom. High-order accuracy requires also edge polynomial moments of the trace of the virtual element functions and their normal derivatives. A set of representative test cases assess the behavior of the method.

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