Energy-Stable Runge–Kutta Schemes for Gradient Flow Models Using the Energy Quadratization Approach
Document Type
Article
Journal/Book Title/Conference
Applied Mathematics Letters
Volume
94
Publisher
Elsevier Ltd
Publication Date
2-13-2019
Award Number
NSF, Division of Mathematical Sciences 1816783
Funder
NSF, Division of Mathematical Sciences
First Page
224
Last Page
231
Abstract
In this letter, we present a novel class of arbitrarily high-order and unconditionally energy-stable algorithms for gradient flow models by combining the energy quadratization (EQ) technique and a specific class of Runge–Kutta (RK) methods, which is named the EQRK schemes. First of all, we introduce auxiliary variables to transform the original model into an equivalent system, with the transformed free energy a quadratic functional with respect to the new variables and the modified energy dissipative law is conserved. Then a special class of RK methods is employed for the reformulated system to arrive at structure-preserving time-discrete schemes. Along with rigorous proofs, numerical experiments are presented to demonstrate the accuracy and unconditionally energy-stability of the EQRK schemes.
Recommended Citation
Gong, Yuezheng, and Jia Zhao. “Energy-Stable Runge–Kutta Schemes for Gradient Flow Models Using the Energy Quadratization Approach.” Applied Mathematics Letters, vol. 94, Aug. 2019, pp. 224–31. DOI.org (Crossref), doi:10.1016/j.aml.2019.02.002.
