汇报标题：Energy-and helicity-conserving enriched Galerkin method for Navier-Stokes equations（Navier-Stokes方程的能量与螺旋度守恒加强伽辽金步骤）
汇报人 (Speaker)：张倩 教授（吉林大学）
汇报功夫 (Time)：2025年12月18日（周四）9:00
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：刘东杰
主办部门：理学院数学系
汇报提要：In this talk, I will present an efficient enriched Galerkin (EG) method for the incompressible Navier–Stokes equations. In contrast to existing EG formulations, our approach enriches the first-order continuous Galerkin space with piecewise constants defined on edges in two dimensions and on faces in three dimensions. This enrichment acts as a correction to the normal component of the CG velocity space, enabling an inf-sup stable discretization. Building on this enriched space, we employ a velocity reconstruction operator and discretize the convective term in its rotational form. This leads to two time-stepping schemes that preserve both discrete kinetic energy and helicity in the inviscid limit: a fully nonlinear Crank–Nicolson scheme, and a linear, computationally cheaper variant obtained by temporally linearizing the convective term.
