Metraipolis › archive › dc_dcc2cebbcf6d

Galerkin finite element method for time fractional diffusion-wave equations with constant time delay — arXiv:2610.21056

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.21056
License (as archived): CC0-1.0
Archived: 2026-10-16T10:32:10.273Z
SHA-256 of the archived text: 495d410e4b958c269741fd351cb96ac50c35c3e14b721692b19cb9a6a27b27c0
Stable URL of this page: https://metraipolis.com/documento/dc_dcc2cebbcf6d

How to cite

Galerkin finite element method for time fractional diffusion-wave equations with constant time delay — arXiv:2610.21056 — arXiv (en), https://arxiv.org/abs/2610.21056 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_dcc2cebbcf6d (Metraipolis archive dc_dcc2cebbcf6d, sha256 495d410e4b958c269741fd351cb96ac50c35c3e14b721692b19cb9a6a27b27c0)

BibTeX

@misc{dcdcc2cebbcf6d,
  title = {Galerkin finite element method for time fractional diffusion-wave equations with constant time delay — arXiv:2610.21056},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.21056},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_dcc2cebbcf6d; sha256 495d410e4b958c269741fd351cb96ac50c35c3e14b721692b19cb9a6a27b27c0},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.21056. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper studies numerical methods for the time fractional diffusion-wave equations with the constant delay. Using a symmetric fractional-order reduction technique and introducing the auxiliary variable $w$, we reformulate the original problem as an equivalent coupled system and for the first time carry out a rigorous regularity analysis of $w$. Based on the symmetric graded time mesh, the coupled problem is discretised by the $L1$ scheme in time and a standard finite element method in space, and the stability result of the developed fully discrete finite element scheme is established by means of a discrete fractional Grönwall inequality. Furthermore, we derive a new comparison principle and reconstruct a new barrier function on each interval $((k-1)\tau,k\tau]$, $1\le k\le K$ according to the properties of the symmetric graded mesh. Based on the new barrier function, we obtain new relevant properties, which lead to a novel and crucial stability property for the discrete fractional operator. Combining the obtained local truncation error in time gives a local error estimate for the fully discrete finite element scheme, which shows that our convergence result provides a unified framework that seamlessly encompasses both pointwise-in-time error estimates on uniform meshes and global-in-time error estimates on symmetrical graded meshes. Numerical experiments confirm the theoretical results.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.NA, nuovi lavori del giorno).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2610.21056 — 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 2026-10-16T08:50:32.695Z dalla pagina https://arxiv.org/list/math.NA/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).