CONTINUOUS FINITE ELEMENTS SATISFYING A STRONG DISCRETE MIRANDA–TALENTI IDENTITY

：田舒丹（湘潭大学）
：2025-07-24 08:00
：海韵园行政楼C503

报 告 人：田舒丹（湘潭大学）

时  间：2025年7月24日8:00

地  点：海韵园行政楼C503

内容摘要:

This talk will introduces continuous H2 -nonconforming finite elements in two and three space dimensions which satisfy a strong discrete Miranda– Talenti inequality in the sense that the global L2 norm of the piecewise Hessian is bounded by the L2 norm of the piecewise Laplacian. The construction is based on globally continuous finite element functions with C1 continuity on the vertices (2D) or edges (3D). As an application, these finite elements are used to approximate uniformly elliptic equations in non-divergence form under the Cordes condition without additional stabilization terms. For the biharmonic equation in three dimensions, the proposed methods has less degrees of freedom than existing nonconforming schemes of the same order. Numerical results in two and three dimensions confirm the practical feasibility of the proposed schemes.

个人简介：

田舒丹，湘潭大学副教授。2021年博士毕业于北京大学。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)。

 

联系人：谭志裕