Abstract
This paper presents an unconditional energy-stable method for the Swift-Hohenberg equation over arbitrarily curved surfaces. We directly define the Laplace–Beltrami operator on the triangular mesh and its dual mesh, which are the discretizations of regular surface. The direct discretization method has several advantages including intrinsic geometry, convergence property, and mass conservation. A second-order temporal accuracy method has been proposed with the Crank-Nicolson type formulation. We have applied the stabilized splitting method to solve the governing system. Our proposed scheme is easy to implement since the two elliptic equations are both linear with low computational burden. The proposed scheme is provable to be Unconditional energy-stable. Several computational tests are conducted to demonstrate that the numerical method is efficient.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
