Metraipolis › archive › dc_faafaaf6f8a3

An Interface Green's Function Framework for Complete Discrete $W^{1,\infty}$ Analysis of Discontinuous Galerkin Methods — arXiv:2608.11559

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.11559
License (as archived): CC0-1.0
Archived: 2026-10-19T05:47:32.765Z
SHA-256 of the archived text: bedb961012dc2091a973c365bd6f8768dbda1592a64a91820bff9ed48fbbe333
Stable URL of this page: https://metraipolis.com/documento/dc_faafaaf6f8a3

How to cite

An Interface Green's Function Framework for Complete Discrete $W^{1,\infty}$ Analysis of Discontinuous Galerkin Methods — arXiv:2608.11559 — arXiv (en), https://arxiv.org/abs/2608.11559 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_faafaaf6f8a3 (Metraipolis archive dc_faafaaf6f8a3, sha256 bedb961012dc2091a973c365bd6f8768dbda1592a64a91820bff9ed48fbbe333)

BibTeX

@misc{dcfaafaaf6f8a3,
  title = {An Interface Green's Function Framework for Complete Discrete $W^1,infty$ Analysis of Discontinuous Galerkin Methods — arXiv:2608.11559},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.11559},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_faafaaf6f8a3; sha256 bedb961012dc2091a973c365bd6f8768dbda1592a64a91820bff9ed48fbbe333},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.11559. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Pointwise error analysis of discontinuous Galerkin (DG) methods for the Poisson equation has received considerable attention during the past two decades. However, on convex polyhedral domains, existing analyses can only establish optimal error estimates in the broken $W^{1,\infty}$ seminorm for several DG methods. Since the broken $W^{1,\infty}$ seminorm does not control discontinuities across mesh interfaces, a complete discrete $W^{1,\infty}$ theory for discontinuous approximations on convex polyhedral domains has remained unavailable. In this paper, we develop an interface Green's function framework for the complete discrete $W^{1,\infty}$ analysis of DG methods on convex polyhedral domains. The proposed framework introduces new interface Green's functions that represent jumps of discontinuous approximations across mesh interfaces. Its central analytical ingredient is a new local energy estimate for these Green's functions, obtained by exploiting a cancellation between neighboring discrete delta functions. This estimate differs fundamentally from existing Green's function estimates and enables us to derive maximum-norm estimate for interface jumps without introducing additional logarithmic factors.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-13 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2608.11559 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T05:40:18.087Z dalla pagina https://arxiv.org/catchup/math.NA/2026-08-13?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).