An energy-stable generalized-α method for the Swift-Hohenberg equation
Access Status
Open access
Authors
Sarmiento, A.
Espath, L.
Vignal, P.
Dalcin, L.
Parsani, M.
Calo, Victor
Date
2017Type
Journal Article
Metadata
Show full item recordCitation
Sarmiento, A. and Espath, L. and Vignal, P. and Dalcin, L. and Parsani, M. and Calo, V. 2017. An energy-stable generalized-α method for the Swift-Hohenberg equation. Journal of Computational and Applied Mathematics. 344: pp. 836-851.
Source Title
Journal of Computational and Applied Mathematics
ISSN
School
School of Earth and Planetary Sciences (EPS)
Collection
Abstract
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-a 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.
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