A new numerical technique to deal with nonlinear terms in gradient flows by introducing a scalar auxiliary variable (SAV), which can construct unconditionally second-order energy stable schemes and can easily construct even third or fourth order BDF schemes, although not unconditionally stable, which are very robust in practice.Expand

We carry out convergence and error analysis of the scalar auxiliary variable (SAV) methods for $L^2$ and $H^{-1}$ gradient flows with a typical form of free energy. We first derive $H^2$ bounds,… Expand

The lack of vertex labeling results in a nontrivial geometry for the space of unlabeled networks, which in turn is found to have important implications on the types of probabilistic and statistical results that may be obtained and the techniques needed to obtain them.Expand

This work concerns the problem associated with an averaging principle for
two-time-scales stochastic partial differential equations (SPDEs) driven
by cylindrical Wiener processes and Poisson random… Expand

The averaging principle for multivalued stochastic differential equations (MSDEs) driven by Brownian motion with Brownian noise is investigated. An averaged MSDEs for the original MSDEs is proposed,… Expand

We introduce an iterative scheme to solve the Yamabe equation −a∆gu+Su = λu p−1 on small domains (Ω, g) ⊂ R equipped with a Riemannian metric g. Thus g admits a conformal change to a constant scalar… Expand

Gradient flows with strong anisotropic free energy are difficult to deal with numerically with existing approaches. We propose a stabilized predictor-corrector approach to construct schemes which are… Expand

It is proved that the schemes are mass conservative, uniquely solvable and keep positivity unconditionally, and the first-order scheme is proven to be unconditionally energy dissipative.Expand