Uzunca, MuratSariaydin-Filibelioglu, Ayse2025-03-232025-03-2320212155-32892155-3297https://doi.org/10.3934/naco.2020025https://hdl.handle.net/11486/4628We 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.eninfo:eu-repo/semantics/openAccessAdvective Allen-Cahn equationdiscontinuous Galerkin methodRothe's methodadaptivityArticle11226928110.3934/naco.20200252-s2.0-85108638816Q1WOS:000624875400005N/A