1 citations · 1 across the 5 of their papers we have counts for
5 papers
Numerical analysis of parabolic equations with Prandtl--Ishlinskii hysteresis of play type
Shu Xu, Liqun Cao
Rigorous error analysis for numerical approximations of parabolic equations with hysteresis remains limited, even for the widely used Prandtl--Ishlinskii model of play type. In thi…
A fourth-order multi-scale computational method and its convergence analysis for composite Kirchhoff plates with microscopic periodic configurations
Hao Dong, Liqun Cao
The Kirchhoff plate model plays a vital role in modeling, computing and analyzing the mechanical behaviors of thin plate structures. This study propose a novel fourth-order multi-s…
Smoothing Newton Methods for Evolving Piecewise Smooth Systems Arising from Parabolic PDEs with Hysteresis
Shu Xu, Liqun Cao
Implicit discretizations of parabolic partial differential equations with hysteresis pose significant challenges for the design of robust nonlinear solvers due to the underlying hi…
Optimal-rate error estimates and a twice decoupled solver for a backward Euler finite element scheme of the Doyle-Fuller-Newman model of lithium-ion cells
Shu Xu, Liqun Cao
We investigate the convergence of a backward Euler finite element discretization applied to a multi-domain and multi-scale elliptic-parabolic system, derived from the Doyle-Fuller-…
Optimal convergence in finite element semi-discrete error analysis of the Doyle-Fuller-Newman model beyond 1D with a novel projection operator
Shu Xu, Liqun Cao
We present a finite element semi-discrete error analysis for the Doyle-Fuller-Newman model, which is the most popular model for lithium-ion batteries. Central to our approach is a…