Abstract
In this paper, an energy-stable finite element method with the Crank–Nicolson type of temporal discretization scheme is developed and analyzed for a class of nonlinear fourth-order parabolic equations (including the Swift–Hohenberg (SH) equation and the extended Fisher–Kolmogorov (EFK) equation). In addition to the energy stability properties, the optimal spatial convergence properties in both L∞(L2)- and L∞(H1)-norm and the second-order temporal approximation rate are also obtained for numerical solutions approximating to the real solution and its Laplacian for the developed energy-stable finite element method in both semi- and fully discrete schemes. Numerical experiments are carried out to validate all attained theoretical results.
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.
