Li-Na Yan

Positivity-preserving scalar auxiliary variable schemes for gradient flows via a quadratic reformulation

The scalar auxiliary variable (SAV) method replaces the nonlinear part of the free energy by a positive scalar $r(t)=\sqrt{\mathcal{E}_{_\mathcal{N}}[\phi]+C}>0$, thereby yielding linear, unconditionally energy-stable schemes for gradient flows. At the discrete level, however, the standard backward Euler and Crank--Nic...