Convergence and error analysis for numerical approximations of stochastic Leray-Lions equations
Abstract
We analyse a divergence form stochastic differential equation featuring a Leray-Lions flux function that satisfies standard Carathéodory, growth, monotonicity, and coercivity conditions. We consider two types of noise: multiplicative Lipschitz continuous noise and a transport noise. Our approach utilises the gradient discretisation method, a generic framework encompassing various numerical schemes such as conforming and nonconforming finite element methods, hybrid mimetic mixed methods, and hybrid high order methods. For both types of noise, we propose a stable generic scheme, prove that scheme solutions converge to a strong solution in the probabilistic sense. For the multiplicative Lipschitz continuous noise, we establish the rate of convergence.
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BibTeX
@misc{le2026convergence,
title = {{Convergence and error analysis for numerical approximations of stochastic Leray-Lions equations}},
author = {Ngan Le and Huateng Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05171},
eprint = {2610.05171},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05171},
}
RIS
TY - UNPB
TI - Convergence and error analysis for numerical approximations of stochastic Leray-Lions equations
AU - Ngan Le
AU - Huateng Zhu
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05171
UR - https://arxiv.org/abs/2610.05171
AB - We analyse a divergence form stochastic differential equation featuring a Leray-Lions flux function that satisfies standard Carathéodory, growth, monotonicity, and coercivity conditions. We consider two types of noise: multiplicative Lipschitz continuous noise and a transport noise. Our approach utilises the gradient discretisation method, a generic framework encompassing various numerical schemes such as conforming and nonconforming finite element methods, hybrid mimetic mixed methods, and hybrid high order methods. For both types of noise, we propose a stable generic scheme, prove that scheme solutions converge to a strong solution in the probabilistic sense. For the multiplicative Lipschitz continuous noise, we establish the rate of convergence.
ER -