Pith Number

pith:GHRRACOJ

pith:2026:GHRRACOJBW7AMXJHPK44SRUFLG

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Fully Discrete High-Order DG Scheme for Waves: Dispersion and Observability

Enrique Zuazua, Xiaoyang Wang, Yunzhang Li

Fully discrete high-order DG schemes for the wave equation exhibit a dispersion-based trapping mechanism leading to exponential blow-up of the observability constant.

arxiv:2605.17464 v1 · 2026-05-17 · math.OC

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Claims

C1strongest claim

Characterizing the coupled space-time numerical dispersion reveals a trapping mechanism that forces the group velocities of both physical and spurious modes to vanish at selected frequencies. We then establish an exponential blow-up of order exp(h^{-(1-ε)}) for the observability constant under this trapping mechanism. To overcome this divergence for arbitrary k, we propose a spectral filtering strategy to restore uniform observability.

C2weakest assumption

The paper assumes that the fully discrete (space-time) dispersion relation for the P^k DG scheme produces vanishing group velocities at selected frequencies, which is the premise used to derive the exponential blow-up of the observability constant.

C3one line summary

Fully discrete DG schemes for the 1D wave equation show dispersion-induced trapping of physical and spurious modes, producing exp(h^{-(1-ε)}) blow-up in observability constants; spectral filtering restores uniform observability, with higher-order methods reducing the filtering burden.

References

37 extracted · 37 resolved · 0 Pith anchors

[1] 1995 , PAGES = 1995

[2] 2014 , PAGES = 2014

[3] Zuazua, Enrique , TITLE =. SIAM Rev. , FJOURNAL =. 2005 , NUMBER = 2005

[4] Infante, Juan Antonio and Zuazua, Enrique , TITLE =. M2AN Math. Model. Numer. Anal. , FJOURNAL =. 1999 , NUMBER = 1999

[5] Micu, Sorin , TITLE =. Numer. Math. , FJOURNAL =. 2002 , NUMBER = 2002

Receipt and verification

First computed	2026-05-20T00:04:40.339241Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31e31009c90dbe065d277ab9c9468559983e802c67a703dc72c8f45e5dc054b1

Aliases

arxiv: 2605.17464 · arxiv_version: 2605.17464v1 · doi: 10.48550/arxiv.2605.17464 · pith_short_12: GHRRACOJBW7A · pith_short_16: GHRRACOJBW7AMXJH · pith_short_8: GHRRACOJ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GHRRACOJBW7AMXJHPK44SRUFLG \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 31e31009c90dbe065d277ab9c9468559983e802c67a703dc72c8f45e5dc054b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e67d22792119f446896c4eda5165cedd40a61b5def8aabbe110f91ade0f85bab",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-17T14:06:53Z",
    "title_canon_sha256": "03f722cc960c23c6108ef4ed347565b6fbec40be3e9224fd29327a944c4518d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17464",
    "kind": "arxiv",
    "version": 1
  }
}