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Time-space adaptive method of time layers for the advective Allen-Cahn equation. (English) Zbl 1387.76061
Karasözen, Bülent (ed.) et al., Numerical mathematics and advanced applications – ENUMATH 2015. Selected papers based on the presentations at the European conference, Ankara, Turkey, September 14–18, 2015. Cham: Springer (ISBN 978-3-319-39927-0/hbk; 978-3-319-39929-4/ebook). Lecture Notes in Computational Science and Engineering 112, 175-183 (2016).
Summary: 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.
For the entire collection see [Zbl 1358.65003].
76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76Txx Multiphase and multicomponent flows
Full Text: DOI arXiv
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