Optimal Error Estimates of a Discontinuous Galerkin Method for Stochastic Allen-Cahn Equation Driven by Multiplicative Noise
Year: 2024
Author: Xu Yang, Weidong Zhao, Wenju Zhao
Communications in Computational Physics, Vol. 36 (2024), Iss. 1 : pp. 133–159
Abstract
In this paper, we develop and analyze an efficient discontinuous Galerkin method for stochastic Allen-Cahn equation driven by multiplicative noise. The proposed method is realized by symmetric interior penalty discontinuous Galerkin finite element method for space domain and implicit Euler method for time domain. Several new estimates and techniques are developed. Under some suitable regularity assumptions, we rigorously establish strong convergence results for the proposed fully discrete numerical scheme and obtain optimal convergence rates in both space and time. Numerical experiments are also carried out to validate our theoretical results and demonstrate the effectiveness of the proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0280
Communications in Computational Physics, Vol. 36 (2024), Iss. 1 : pp. 133–159
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Stochastic Allen-Cahn equation strong convergence discontinuous Galerkin method variational solution multiplicative noise.
Author Details
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Legendre spectral volume methods for Allen–Cahn equations by the direct discontinuous Galerkin formula
Guan, Chaoyue
Sun, Yuli
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https://doi.org/10.1016/j.aml.2024.109382 [Citations: 0]