»ã±¨±êÌâ (Title)£ºModel and data-driven fully discrete continuous data assimilation algorithms: error estimates and parameter recovery (Ä£ÐͺÍÊý¾ÝÇý¶¯µÄÆëÈ«Àëɢ½ÐøÊý¾Ýͬ»¯Ëã·¨£ºÎó²î¹À¼ÆºÍ²ÎÊý¸´Ô­)

»ã±¨ÈË (Speaker)£ºÍõÍíÉú½ÌÊÚ (ÉϺ£Ê¦·¶´óѧ)

»ã±¨¹¦·ò (Time)£º2025Äê11ÔÂ13ÈÕ£¨ÖÜËÄ£©10:00

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒé 985 273 770

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The purpose of this study is to provided error estimates for model and data-driven fully discrete continuous data assimilation algorithms for reaction-diffusion equations and 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 (IMEX) 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 methods plays key roles in proving the exponential decay of initial error. Based on the long-time error estimates, we develop several algorithms to recover both the true solution and the true diffuse interface width using only spatially discrete phase field function measurements. Numerical experiments confirm our theoretical results and verify the effectiveness of the proposed methods.