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High Order Whitney Forms on Simplices and the Question of Potentials Read chapter Read first chapter

2021 | OriginalPaper | Chapter

Study on an Adaptive Finite Element Solver for the Cahn–Hilliard Equation

Authors : G. Fabian Castelli, Willy Dörfler

Published in: Numerical Mathematics and Advanced Applications ENUMATH 2019

Publisher: Springer International Publishing

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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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previous chapter Local Flux Reconstruction for a Frictionless Unilateral Contact Problem
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Metadata
Title
Study on an Adaptive Finite Element Solver for the Cahn–Hilliard Equation
Authors
G. Fabian Castelli
Willy Dörfler
Copyright Year
2021
Book
Numerical Mathematics and Advanced Applications ENUMATH 2019

Print ISBN: 978-3-030-55873-4

Electronic ISBN: 978-3-030-55874-1

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-55874-1_23

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