Mathematics > Numerical Analysis
[Submitted on 15 Jan 2019 (v1), last revised 16 Jan 2020 (this version, v2)]
Title:Adaptive Discontinuous Galerkin Finite Elements for Advective Allen-Cahn Equation
View PDFAbstract:We apply a space adaptive interior penalty discontinuous Galerkin method for solving advective Allen-Cahn equation with expanding and contracting velocity fields. The advective Allen-Cahn equation is first discretized in time and the resulting semi-linear elliptic PDE is solved by an adaptive algorithm using a residual-based a posteriori error estimator. The a posteriori error estimator contains additional terms due to the non-divergence-free velocity field. Numerical examples demonstrate the effectiveness and accuracy of the adaptive approach by resolving the sharp layers accurately.
Submission history
From: Murat Uzunca [view email][v1] Tue, 15 Jan 2019 15:59:30 UTC (1,211 KB)
[v2] Thu, 16 Jan 2020 15:14:27 UTC (1,677 KB)
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