»ã±¨±êÌâ (Title)£ºAnalysis of fully discrete finite element methods for 2D Navier--Stokes equations with critical initial data(ÓµÓÐÁÙ½ç³õʼֵµÄ¶þάNavier-Stokes·½³ÌµÄÈ«ÀëÉ¢ÓÐÏÞÔª·¨µÄ·ÖÎö)

»ã±¨ÈË (Speaker)£º Àî²½Ñï ¸±½ÌÊÚ£¨Ïã¸ÛÀí¹¤´óѧ£©

»ã±¨¹¦·ò (Time)£º2022Äê9ÔÂ9ÈÕ(ÖÜÎå) 14:00-16:00

»ã±¨µØÖ· (Place)£ºÏßÉÏÌÚѶ»áÒé £¨»áÒé ID£º963 935 431£©

Ô¼ÇëÈË(Inviter)£ºÀƷ¡¢²ÌÃô

Ö÷°ì²¿ÃÅ£ºÀíѧԺÊýѧϵ

»ã±¨ÌáÒª£ºFirst-order convergence in time and space is proved for a fully discrete semi-implicit finite element method for the two-dimensional Navier--Stokes equations with $L^2$ initial data in convex polygonal domains, without extra regularity assumptions or grid-ratio conditions. The proof utilises the smoothing properties of the Navier--Stokes equations in the analysis of the consistency errors, an appropriate duality argument, and the smallness of the numerical solution in the discrete $L^2(0,t_m;H^1)$ norm when $t_m$ is smaller than some constant. Numerical examples are provided to support the theoretical analysis.