A New L2-Gradient Flow-Based Fractional-in-Space Modified Phase-Field Crystal Equation and Its Mass Conservative and Energy Stable Method

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Abstract

In this paper, we introduce a new fractional-in-space modified phase-field crystal equation based on the (Formula presented.) -gradient flow approach, where the mass of atoms is conserved by using a nonlocal Lagrange multiplier. To solve the (Formula presented.) -gradient flow-based fractional-in-space modified phase-field crystal equation, we present a mass conservative and energy stable method based on the convex splitting idea. Numerical examples together with standard tests in the classical (Formula presented.) -gradient flow-based modified phase-field crystal equation are provided to illustrate the applicability of the proposed framework.

Original languageEnglish
Article number472
JournalFractal and Fractional
Volume6
Issue number9
DOIs
StatePublished - Sep 2022

Keywords

  • convex splitting
  • energy stability
  • fractional-in-space modified phase-field crystal equation
  • L-gradient flow
  • mass conservation
  • nonlocal Lagrange multiplier
  • unique solvability

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