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An enhanced finite element technique for diffuse phase transition

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Abstract

We propose a finite element technique to enhance phase-field simulations. As adaptive p-method it and can be generally applied to finite element formulations. However, diffuse interfaces have non-linear gradients within regions typically smaller compared to the size of the overall model. Thus, enhanced field interpolation with higher polynomial functions on demand allows for coarser meshing or lower regularization length for the phase transition. Our method preserves \(C^0\) continuity of finite elements and is particularly advantageous in the context of parallelized computing. An analytical solution for the evolution of a phase-field variable governed by the Allen–Cahn equation is used to define an error measure and to investigate the proposed method. Several examples demonstrate the capability of this finite element technique.

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Notes

  1. This guarantees symmetric matrices \(\mathbf{{K}}_{elem}\) and \(\mathbf{{D}}_{elem}\) in Eq. 35.

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Authors and Affiliations

  1. Institute for Structural Analysis, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76131, Karlsruhe, Germany

    I. Münch & M. Krauß

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  1. I. Münch
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  2. M. Krauß
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Correspondence to I. Münch.

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Münch, I., Krauß, M. An enhanced finite element technique for diffuse phase transition. Comput Mech 56, 691–708 (2015). https://doi.org/10.1007/s00466-015-1195-5

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  • DOI: https://doi.org/10.1007/s00466-015-1195-5

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