Computational Mechanics

, Volume 56, Issue 4, pp 691–708 | Cite as

An enhanced finite element technique for diffuse phase transition

Original Paper


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.


Phase-field modeling Phase transition Adaptive p-method Enhanced finite element method 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute for Structural AnalysisKarlsruhe Institute of Technology (KIT)KarlsruheGermany

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