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High-Moment Stability and Error Analysis of a Fully Discrete LDG-IMEX Method for High Dimensional Nonlinear Stochastic Convection-Diffusion Equations — arXiv:2609.21920

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.21920
License (as archived): CC0-1.0
Archived: 2026-10-10T02:09:48.700Z
SHA-256 of the archived text: 00558daf62694d27c6c936177a389207d71fe509971fe875e7178822305f78e9
Stable URL of this page: https://metraipolis.com/documento/dc_5065af5259c1

How to cite

High-Moment Stability and Error Analysis of a Fully Discrete LDG-IMEX Method for High Dimensional Nonlinear Stochastic Convection-Diffusion Equations — arXiv:2609.21920 — arXiv (en), https://arxiv.org/abs/2609.21920 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_5065af5259c1 (Metraipolis archive dc_5065af5259c1, sha256 00558daf62694d27c6c936177a389207d71fe509971fe875e7178822305f78e9)

BibTeX

@misc{dc5065af5259c1,
  title = {High-Moment Stability and Error Analysis of a Fully Discrete LDG-IMEX Method for High Dimensional Nonlinear Stochastic Convection-Diffusion Equations — arXiv:2609.21920},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.21920},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_5065af5259c1; sha256 00558daf62694d27c6c936177a389207d71fe509971fe875e7178822305f78e9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.21920. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A fully discrete local discontinuous Galerkin (LDG) method coupled with an implicit-explicit (IMEX) Euler time discretization is presented and analyzed for a class of high dimensional nonlinear stochastic convection-diffusion equations driven by multiplicative $\mathcal Q$-Wiener noise. The model allows nonlinear leading coefficients, nonlinear convection terms, dissipative source terms, and gradient-dependent noise. The diffusion operator is treated implicitly through the LDG formulation, while the nonlinear convection, lower-order drift, and stochastic terms are evaluated explicitly. The main contribution is a high-moment stability and error analysis for the fully discrete scheme. A central difficulty is that the nonlinear terms lead to pathwise growth factors that cannot be controlled uniformly on the full sample space. To provide the stability and error estimate, we introduce recursively defined nested subsets adapted to the numerical solution. Under the stated stochastic parabolicity and refinement conditions, we prove that these subsets have probabilities converging to one. On these subsets, the numerical solution satisfies high-moment stability, and the fully discrete error converges with order arbitrarily close to $r+1$ in space and $1/2$ in time. We also derive a pathwise error estimate by combining the high-moment error bound with a discrete Kolmogorov argument. Numerical experiments for stochastic Burgers' and Allen-Cahn equations confirm the theoretical rates and demonstrate the robustness of the proposed method for nonlinear stochastic models.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-21 in math.PR).
Categorie arXiv: Numerical Analysis (math.NA) ; Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.21920 — 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 2026-10-10T01:47:50.229Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-21?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).