Submitted

Hybridizable Staggered Discontinuous Galerkin Methods for Polyharmonic Equations on Polytopes

Long Chen, Xuehai Huang, Yule Sun, and Shudan Tian

Submitted

arXiv   Bibtex

ABSTRACT:

Hybridizable staggered discontinuous Galerkin methods are
developed for arbitrary-order polyharmonic equations $(-\Delta)^m u=f$
on shape-regular polytopal meshes in $\mathbb R^d$, for any $m\ge1$,
$d\ge2$, and polynomial degree $k\ge0$. The method uses the mixed
variable $\sigma=\nabla^m u$ and a staggered primal--dual mesh to
impose complementary continuity on scalar and tensor unknowns, without
restrictions such as $d\ge m$. Local trace and bubble enrichments
stabilize low-order tensor spaces without adding global
unknowns. Hybridization localizes the tensor variable and yields an
equivalent stabilization-free weak Galerkin
formulation. Well-posedness and optimal energy error estimates are
proved, and numerical experiments on polygonal and tetrahedral meshes
confirm the predicted rates.