Time-Space Adaptive Method of Time Layers for the Advective Allen-Cahn Equation

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UZUNCA M., KARASÖZEN B. , Sariaydin-Filibelioglu A.

European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), Ankara, Türkiye, 14 - 18 Eylül 2015, cilt.112, ss.175-183 identifier identifier

  • Cilt numarası: 112
  • Doi Numarası: 10.1007/978-3-319-39929-4_18
  • Basıldığı Şehir: Ankara
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.175-183


We develop an adaptive method of time layers with a linearly implicit Rosenbrock method as time integrator and symmetric interior penalty Galerkin method for space discretization for the advective Allen-Cahn equation with a non-divergence-free velocity field. Numerical simulations for advection-dominated problems demonstrate the accuracy and efficiency of the adaptive algorithm for resolving the sharp layers occurring in interface problems with small surface tension.