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 language | English |
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Article number | 472 |
Journal | Fractal and Fractional |
Volume | 6 |
Issue number | 9 |
DOIs | |
State | Published - 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