Study on an hp‐Adaptive Finite Element Solver for a Chemo‐Mechanical Battery Particle Model

We consider a Cahn–Hilliard-type phase-field model for phase separation and large deformations in battery electrode particles. For the numerical solution we employ an hp-adaptive finite element solution algorithm coupled to a variable-step, variable-order time stepping scheme. Numerical experiments show the adaptive meshing and distribution of the locally varying polynomial degrees of the finite element method. In particular, for a sufficient large range of polynomial degrees we achieve significant computational savings compared to an h-adaptive algorithm.