Unconditional Energy Stability and Solvability for a C0 Interior Penalty Method for a Sixth-Order Equation Modeling Microemulsions
Year: 2023
Author: Amanda E. Diegel, Natasha S. Sharma
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 4 : pp. 459–477
Abstract
We consider a C0 interior penalty finite element approximation of a sixth-order Cahn-Hilliard type equation that models the dynamics of phase transitions in ternary oil-water-surfactant systems. The nonlinear sixth-order parabolic equation is expressed in a mixed form whereby a second-order (in space) parabolic equation and an algebraic fourth-order (in space) nonlinear equation are considered. The temporal discretization is chosen so that a discrete energy law can be established leading to unconditional energy stability. Additionally, we show that the numerical method is unconditionally uniquely solvable. We conclude with several numerical experiments demonstrating the unconditional stability and first-order accuracy of the proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2023-1019
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 4 : pp. 459–477
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Finite element Cahn-Hilliard unconditional energy stability microemulsions and unique solvability.