Scalar auxiliary variable approach for conservative/dissipative partial differential equations with unbounded energy functionals

A Linearly Implicit Structure-Preserving Scheme for the Camassa–Holm Equation Based on Multiple Scalar Auxiliary Variables Approach

(2020) Chaolong Jiang et al.   JOURNAL OF SCIENTIFIC COMPUTING

Arbitrarily high-order linear energy stable schemes for gradient flow models

(2020) Yuezheng Gong et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Energy stability and convergence of SAV block-centered finite difference method for gradient flows

(2019) Xiaoli Li et al.   MATHEMATICS OF COMPUTATION

Arbitrarily high-order unconditionally energy stable SAV schemes for gradient flow models

(2019) Yuezheng Gong et al.   COMPUTER PHYSICS COMMUNICATIONS

Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions

(2019) Wenjun Cai et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Efficient SAV approach for imaginary time gradient flows with applications to one- and multi-component Bose-Einstein Condensates

(2019) Qingqu Zhuang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Efficient modified techniques of invariant energy quadratization approach for gradient flows

(2019) Zhengguang Liu et al.   APPLIED MATHEMATICS LETTERS

A roadmap for discretely energy-stable schemes for dissipative systems based on a generalized auxiliary variable with guaranteed positivity

(2019) Zhiguo Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Novel high-order energy-preserving diagonally implicit Runge–Kutta schemes for nonlinear Hamiltonian ODEs

(2019) Hong Zhang et al.   APPLIED MATHEMATICS LETTERS

The scalar auxiliary variable (SAV) approach for gradient flows

(2018) Jie Shen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows

(2018) Jie Shen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

(2017) Xiaofeng Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach

(2016) Jia Zhao et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends

(2016) Xiaofeng Yang   JOURNAL OF COMPUTATIONAL PHYSICS

Numerical Analysis of Second Order, Fully Discrete Energy Stable Schemes for Phase Field Models of Two-Phase Incompressible Flows

(2016) Daozhi Han et al.   JOURNAL OF SCIENTIFIC COMPUTING

Energy-diminishing integration of gradient systems

(2013) E. Hairer et al.   IMA JOURNAL OF NUMERICAL ANALYSIS

Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method

(2012) E. Celledoni et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A General Framework for Deriving Integral Preserving Numerical Methods for PDEs

(2011) Morten Dahlby et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING