| Abstract: |
| In this paper, we propose and analyze a new generalized scalar auxiliary variable (GSAV) approach to deal with nonlinear terms in $L^{2}$ gradient flows. This new approach can be viewed as an
extension of scalar auxiliary variable (introduced by J. Shen et al) without assumption that $\int_{\Omega}F(\phi)d\mathbf{x}$ is bounded from below.
We construct an efficient and robust first and second order unconditionally energy stable GSAV schemes for gradient flows. Optimal error estimates are established. The explain how GSAV approach
is not restricted to the special forms of the nonlinear terms and only requires to solve decoupled linear system with constant coefficients that can solved using
any fast solver for Poisson equation. Finally several numerical experiments were carried out to verify the theoretical claims and illustrate the efficiency of our method. |
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