Work

The Efficient Variable Time-stepping DLN Algorithms for the Allen-Cahn Model

Year: 2024

Type: preprint

Abstract: We consider a family of variable time-stepping Dahlquist-Liniger-Nevanlinna (DLN) schemes, which is unconditional non-linear stable and second order accurate, for the Allen-Cahn equation. The finite element methods are used for the spatial discretization. For the non-linear term, we combine the DLN scheme with two efficient temporal algorithms: partially implicit modified algorithm and scalar auxiliary variable algorithm. For both approaches, we prove the unconditional, long-term stability of the model energy under any arbitrary time step sequence. Moreover, we provide rigorous error analysis for the partially implicit modified algorithm with variable time-stepping. Efficient time adaptive algorithms based on these schemes are also proposed. Several one- and two-dimensional numerical tests are presented to verify the properties of the proposed time adaptive DLN methods.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2409.19481

Authors: Chen, YiMing, Luo, Dianlun, Pei, Wenlong, Xing, Yulong

Institutions: The Ohio State University, Columbia University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Ohio State University

Awards: Collaborative Research: Arbitrary Order Structure-Preserving Discontinuous Galerkin Methods for Compressible Euler Equations With Self-Gravity in Astrophysical Flows, CAREER: High Order Structure-Preserving Numerical Methods for Hyperbolic Conservation Laws

OpenAlex ID: W4403812517

Cites:

Cited by:

Related to: 10