3 papers
math.NA2025
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…
math.NA2025
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-…
math.NA2025
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…