| Abstract: |
| Recently, a new technique, the single auxiliary variable (SAV)
approach, is proposed to deal with nonlinear terms in a large class of gradient
flows. The technique is not restricted to
specific forms of the
nonlinear part of the free energy, it leads to linear and
unconditionally energy
stable second-order (or higher-order with weak stability conditions)
schemes which only require solving decoupled
linear equations with constant coefficients. Hence, these schemes are
extremely efficient as well as accurate.
We present a convergence and error analysis of the SAV approach ,and
apply the SAV approach to deal with several challenging applications
which can not be easily handled by existing approaches, and present
convincing numerical results to show that the new schemes are not only much
more efficient and easy to implement, but also can better capture
the physical properties in these models. |
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