报告题目：Continuous finite elements satisfying a strong Miranda-Talenti identity

报告时间：2025-03-22   10:30-11:30

报 告 人：田舒丹   副教授  湘潭大学

报告地点：雷军科技楼八楼报告厅（806）

Abstract：This article introduces continuous H2 -nonconforming fifiniteelements in two and three space dimensions which satisfy a strong discrete Miranda–Talentiinequality 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 fifiniteelement functions with C1 continuity on the vertices (2D) or edges (3D). As an application, these fifiniteelements 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 confifirmthe practical feasibility of the proposed schemes.