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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 hysteresis of play type. I…
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…
Parabolic hysteresis problems revisited: Finite element error analysis and convergent Newton-type solvers
Shu Xu, Liqun Cao
Numerical investigations of partial differential equations with hysteresis have largely focused on simulations, leaving numerical error analysis unexplored and relying mainly on de…
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…