报告题目：Raviart–Thomas Enriched Scott–Vogelius Finite Elements for Divergence-Free and Robust Incompressible Flow Simulations

报告人：李旭副研究员山东大学博彩App

报告时间：2026年7月16日10:00--11:00

报告地点：正新楼315

校内联系人：张倩 [email protected]

报告摘要：

    This talk presents a unified finite element framework for incompressible flow problems based on Raviart-Thomas enriched Scott-Vogelius spaces. The key idea is to enrich classical H^1-conforming Lagrange velocity spaces with carefully chosen H(div)-conforming Raviart-Thomas functions, obtaining inf-sup stable schemes on general shape-regular simplicial meshes with exactly divergence-free velocities. The enrichment provides the missing divergence modes while keeping the main velocity component H^1-conforming; moreover, the enrichment unknowns and higher-order pressure unknowns can be locally eliminated, leading to reduced P_k-P_0-type schemes. The framework is further developed for the time-dependent Navier–Stokes equations. Suitable discretizations of the convective term preserve linear and angular momentum in appropriate senses and lead to pressure-robust and convection-robust velocity error estimates. Finally, a decoupled variant is obtained by constructing divergence-free basis functions, allowing the velocity and pressure to be computed separately and replacing the saddle point problem by symmetric positive definite systems. Numerical experiments in two and three dimensions illustrate the accuracy, robustness, and efficiency of the proposed methods.

报告人简介：

    李旭，山东大学博彩App 副研究员。2023年毕业于山东大学博彩App 计算数学专业并获博士学位，2023—2025年在宁波东方理工大学从事博士后研究工作。主要研究偏微分方程数值解及科学计算，重点针对不可压缩流动模型（如Navier–Stokes方程）设计与分析具有稳定性、保结构性和高精度特征的有限元数值方法。在Math. Comp.、M3AS、IMA J. Numer. Anal.等计算数学与应用数学领域权威期刊发表学术论文9篇。主持中国博士后科学基金面上项目（已结题）和国家自然科学基金青年项目（C类）。