WCCM ECCOMAS 2026

H^m Non-Conforming Finite Element Spaces on Polygonal Meshes in Arbitrary Dimensions

Chen, Long (Department of Mathematics, University of Cali)
Huang, XueHai (School of Mathematics, Shanghai University of)
Sun, Yule (School of Mathematics and Computational Scien)
Tian, Shudan (School of Mathematics and Computational Scien)

In session: MS395B - Advanced Structure-preserving Moment Methods and Numerics of Kinetic Equations II

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We propose a novel H^m-nonconforming staggered discontinuous Galerkin (SDG) method for solving m-th order Laplace equations on polytopal meshes in arbitrary dimensions, inspired by the ideas introduced in [1]. The scheme is hybridizable and requires fewer degrees of freedom. Optimal error estimates are established in the energy norm, and the L^2-error convergence can be further improved via post-processing. Numerical experiments are presented to confirm the theoretical convergence rates of the proposed method.