arXiv:2610.41747v1 Announce Type: new Abstract: This paper analyzes a symmetric interior penalty discontinuous Galerkin (IPDG) method, a hybrid mixed DG method, and two representative hybridizable discontinuous Galerkin (HDG) methods for the Poisson problem on convex polyhedral domains. For any fixed $\epsilon\in (0,\frac{1}{2})$, we first derive optimal discrete $W^{1,p}$ error estimates for $2\leq p<\frac{1}{\epsilon}$ by combining the interface Green's functions developed in \cite{lq2026} with the Fubini-type weighted estimates established in this paper. These error estimates lead to discrete $W^{1,q}$-$W^{1,p}$ inf-sup stability for $2\leq q<\frac{1}{\epsilon}$, where $q$ is the conjugate number of $p$ such that $\frac{1}{p}+\frac{1}{q}=1$. Using this stability result and a suitably constructed dual problem, we extend the optimal error estimates to $\frac{1}{1-\epsilon}Source：https://arxiv.org/abs/2610.41747
My favorites