This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …

We propose a new approach, which we term as scalar auxiliary variable (SAV) approach, to
construct efficient and accurate time discretization schemes for a large class of gradient …

In this survey article, a variety of systems modeling tumor growth are discussed. In
accordance with the hallmarks of cancer, the described models incorporate the primary …

We propose a new numerical technique to deal with nonlinear terms in gradient flows. By
introducing a scalar auxiliary variable (SAV), we construct efficient and robust energy stable …

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 …

My purpose in this monograph is to present an essentially self-contained account of the
mathematical theory of Galerkin? nite element methods as appliedtoparabolicpartialdi …

In this paper we construct two classes, based on stabilization and convex splitting, of
decoupled, unconditionally energy stable schemes for Cahn--Hilliard phase-field models of …

We construct and analyze a class of extrapolated and linearized Runge--Kutta (RK)
methods, which can be of arbitrarily high order, for the time discretization of the Allen--Cahn …

In this paper we present and analyze finite difference numerical schemes for the Cahn-
Hilliard equation with a logarithmic Flory Huggins energy potential. Both first and second …

This review concerns the computation of curvature-dependent interface motion governed by
geometric partial differential equations. The canonical problem of mean curvature flow is that …