Adaptive time-stepping and maximum-principle preserving Lagrangian schemes for gradient flows

2025/04/18 by Liu, Qianqian, Chen, Wenbin, Shen, Jie +1
#35K55 #35K65 #65M06 #65M12 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2504.13552

Abstract

We develop in this paper an adaptive time-stepping approach for gradient flows with distinct treatments for conservative and non-conservative dynamics. For the non-conservative gradient flows in Lagrangian coordinates, we propose a modified formulation augmented by auxiliary terms to guarantee positivity of the determinant, and prove that the corresponding adaptive second-order Backward Difference Formulas (BDF2) scheme preserves energy stability and the maximum principle under the time-step ratio constraint 0

Citations

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Related

• Arbitrary High-Order Maximum Principle-Preserving and Energy Dissipating Schemes for Gradient Flows
• An implicit--explicit second order BDF numerical scheme with variable steps for gradient flows
• Two structure-preserving time discretizations for gradient flows
• High Order Schemes for Gradient Flow with Respect to a Metric
• Higher-Order Energy-Decreasing Exponential Time Differencing Runge-Kutta methods for Gradient Flows