An energy-stable generalized- α method for the Swift–Hohenberg equation

Adel Sarmiento, Luis Espath, P. Vignal, Lisandro Dalcin, Matteo Parsani, V.M. Calo

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We propose a second-order accurate energy-stable time-integration method that controls the evolution of numerical instabilities introducing numerical dissipation in the highest-resolved frequencies. Our algorithm further extends the generalized-α method and provides control over dissipation via the spectral radius. We derive the first and second laws of thermodynamics for the Swift–Hohenberg equation and provide a detailed proof of the unconditional energy stability of our algorithm. Finally, we present numerical results to verify the energy stability and its second-order accuracy in time.
Original languageEnglish (US)
Pages (from-to)836-851
Number of pages16
JournalJournal of Computational and Applied Mathematics
StatePublished - Nov 16 2017


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