Abstract
In this work we present an adaptive matrix-free finite element solver for the Cahn–Hilliard equation modelling phase separation in electrode particles of lithium ion batteries during lithium insertion. We employ an error controlled variable-step, variable-order time integrator and a regularity estimator for the adaptive mesh refinement. In particular, we propose a matrix-free applicable preconditioner. Numerical experiments demonstrate the importance of adaptive methods and show for our preconditioner practically no dependence of the number of GMRES iterations on the mesh size, even for locally refined meshes.
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Acknowledgements
The authors thank M. Kamlah and T. Zhang for discussions about the model equations. G.F. Castelli acknowledges financial support by the German Research Foundation (DFG) through RTG 2218 SiMET—Simulation of mechano-electro-thermal processes in lithium-ion batteries, project number 281041241.
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Castelli, G.F., Dörfler, W. (2021). Study on an Adaptive Finite Element Solver for the Cahn–Hilliard Equation. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_23
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