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Research Article | Open Access

A weak Galerkin method for nonlinear stochastic parabolic partial differential equations with additive noise

Hongze Zhu1( ), Chenguang Zhou2, Nana Sun3
School of Science, Shandong Jianzhu University, Jinan 250101, Shandong, China
Faculty of Science, Beijing University of Technology, Beijing 100124, China
Dongjia Primary School, Jinan 250101, Shandong, China
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Abstract

In this paper, a weak Galerkin (WG for short) finite element method is used to approximate nonlinear stochastic parabolic partial differential equations with spatiotemporal additive noises. We set up a semi-discrete WG scheme for the stochastic equations, and derive the optimal order for error estimates in the sense of strong convergence.

Keywords

weak Galerkin finite element methodLipschitz continuitynonlinear stochastic partial differential equationQ-Wiener processadditive noise

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Electronic Research Archive
Volume 30 Issue 6,
June 2022
Pages 2321-2334
DOI: 10.3934/era.2022118

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Cite this article:
Zhu H, Zhou C, Sun N. A weak Galerkin method for nonlinear stochastic parabolic partial differential equations with additive noise. Electronic Research Archive, 2022, 30(6): 2321-2334. https://doi.org/10.3934/era.2022118

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Received: 22 August 2021
Revised: 17 February 2022
Accepted: 17 February 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)