Host: Jiang Hu

Abstract: This talk will introduce stable finite element pairs for the linear stress gradient elasticity model, overcoming classical elasticity's limitations in capturing size effects. We analyze mesh conditions to establish parameter-robust error estimates for the proposed pairs. For finite elements with higher vertex continuity, stability is obtained without imposing conditions on the mesh geometry. For CG--DG pairs, stability holds when no interior vertex has edges lying on three or fewer distinct lines. Numerical experiments validate the theoretical results, demonstrating optimal convergence rates.

Bio: 田舒丹，2021年博士毕业于北京大学，于2021年--2023年在德国耶拿大学从事博士后，现于湘潭大学任教。主要从事非标准有限元方法研究，包括微结构弹性力学问题、奇异摄动问题、四阶椭圆问题、Stokes问题的有限元方法。在SIAM J. SCI. COMPUT，IMA J. Numer Anal，Sci. China等数学刊物发表论文多篇。目前正在主持国家自然科学青年基金(C类)。