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
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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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