Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms
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Wansheng Wang,
Chengyu Jin,
Yunqing Huang
Abstract:The purpose of this study is to recover the diffuse interface width parameter for nonlinear Allen–Cahn equation by a continuous data assimilation algorithm proposed recently. We obtain the large-time error between the true solution of the Allen–Cahn equation and the data assimilated solution produced by implicit–explicit one-leg fully discrete finite element methods due to discrepancy between an approximate diffuse interface width and the physical interface width. The strongly A-stability of the one-leg method… Show more
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