报告题目：求解时变广义Boussinesq方程的分数步DG-FE方法
Title: A fractional-step DG-FE method for time-dependent generalized Boussinesq equations
报告人 (Speaker)：侯源远 博士（湖州师范学院）
报告时间 (Time)：2025年12月5日(周五) 15：00
报告地点 (Place)：腾讯会议：859-218-246（会议密码：1205）
邀请人(Inviter)：刘东杰
报告摘要：In this work a fractional-step DG-FE method for the time-dependent generalized Boussinesq equations is proposed and analysed. The scheme is composed of two steps. In the first step the original problem is reduced into several scalar elliptic equations. An intermediate velocity and temperature are solved simultaneously. Then in the second step, the incompressibility constraint is enforced and velocity is corrected to be discretely divergence free. Moreover, the introduced elliptic term in the correction step enables the imposition of correct Dirichlet boundary conditions at each temporal step, avoiding the artificial boundary layer introduced by classical pressure correction method. DG-FE discretization strategy is utilized, in which the discontinuous Galerkin spacial discretization for flow equations is employed to obtain local mass conservation and traditional finite element spacial discretization is adopted for heat equation to reduce degrees of freedom. By choosing different symmetry and penalty parameters, SIPG-FE and NIPG-FE methods can be utilized. The consistency and stability of both methods are proved. Preliminary error estimates proving the optimal spacial order and suboptimal temporal order are carried out. Based on a different error equation and the preliminary error estimates, the optimal temporal convergence order is obtained. Numerical tests including a benchmark simulating square cavity flow are then presented, to verify the theoretical analysis and validate the method.