605 citations · 1.2k across the 29 of their papers we have counts for
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Unconditional Optimal Error Estimates and Energy Stability for a Linearly Implicit Mass-Lumped Projection Finite Element Method for the Harmonic Map Flow
Yongyong Cai, Xingwei Yang
We propose and analyze a linearly implicit mass-lumped finite element method for the heat flow of harmonic maps into the unit sphere. The method consists of a linear predictor foll…
A robust hybridizable discontinuous Galerkin scheme with harmonic averaging technique for steady state of real-world semiconductor devices
Qingyuan Shi, Yongyong Cai, Chijie Zhuang +4
Solving real-world nonlinear semiconductor device problems modeled by the drift-diffusion equations coupled with the Poisson equation (also known as the Poisson-Nernst-Planck equat…
Stabilized exponential time differencing schemes for the convective Allen-Cahn equation
Yongyong Cai, Lili Ju, Rihui Lan +1
The convective Allen-Cahn equation has been widely used to simulate multi-phase flows in many phase-field models. As a generalized form of the classic Allen-Cahn equation, the conv…
Improved uniform error bounds on time-splitting methods for the long-time dynamics of the weakly nonlinear Dirac equation
Weizhu Bao, Yongyong Cai, Feng Yue
Improved uniform error bounds on time-splitting methods are rigorously proven for the long-time dynamics of the weakly nonlinear Dirac equation (NLDE), where the nonlinearity stren…
Convergence Analysis of A Second-order Accurate, Linear Numerical Scheme for The Landau-Lifshitz Equation with Large Damping Parameters
Yongyong Cai, Jingrun Chen, Cheng Wang +1
A second order accurate, linear numerical method is analyzed for the Landau-Lifshitz equation with large damping parameters. This equation describes the dynamics of magnetization,…
Improved uniform error bounds on time-splitting methods for long-time dynamics of the nonlinear Klein--Gordon equation with weak nonlinearity
Weizhu Bao, Yongyong Cai, Yue Feng
We establish improved uniform error bounds on time-splitting methods for the long-time dynamics of the nonlinear Klein--Gordon equation (NKGE) with weak cubic nonlinearity, whose s…