Stability and Error estimates of the SAV Fourier-spectral method for the Phase Field Crystal Equation

2019/07/17 by Xiaoli Li, Jie Shen, Li, Xiaoli +1 · 2 citations
Engineering · Materials Science · Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Fluid Dynamics and Thin Films #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.1907.07462

openalex publication_date 2019/07/17 · openalex created_date 2019/07/23 · openalex updated_date 2026/07/31

Abstract

We consider fully discrete schemes based on the scalar auxiliary variable (SAV) approach and stabilized SAV approach in time and the Fourier-spectral method in space for the phase field crystal (PFC) equation. Unconditionally energy stability is established for both first- and second-order fully discrete schemes. In addition to the stability, we also provide a rigorous error estimate which shows that our second-order in time with Fourier-spectral method in space converges with order O(Δt²+N^-m), where Δt, N and m are time step size, number of Fourier modes in each direction, and regularity index in space, respectively. We also present numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy of the schemes.

Citations

• Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows

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