Numerical Analysis of Stochastic Elliptic Variational Inequalities of the First Kind

Chenhui Zhu; Fei Wang; Weimin Han

doi:10.1016/j.cam.2026.117950

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Numerical Analysis of Stochastic Elliptic Variational Inequalities of the First Kind

Journal article

Peer reviewed

Numerical Analysis of Stochastic Elliptic Variational Inequalities of the First Kind

Chenhui Zhu, Fei Wang and Weimin Han

Journal of computational and applied mathematics, Vol.490, 117950

01/15/2027

DOI: 10.1016/j.cam.2026.117950

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Abstract

This paper presents a numerical approach to the stochastic obstacle problem using the stochastic Galerkin (SG) method. Due to the low regularity of the solution, linear finite elements are employed in both the physical and random variable spaces. Properties of random fields and variational inequalities of the first kind are employed to establish the well-posedness of the problem. Finite element spaces are introduced to construct suitable approximation subspaces, and a comprehensive SG formulation is proposed to solve the stochastic obstacle problem. Well-posedness of the discrete formulation is shown and an optimal error estimate for the numerical solution in the H1-norm is derived. Numerical experiments validate the effectiveness of the SG method, showing that both the expectation error and the second moment error converge at a rate of O(h) in the H1-norm, consistent with theoretical predictions.

65C20

65K15

65N12

65N30

a priori error estimate

AMSSC

obstacle problem

Stochastic elliptic variational inequalities

stochastic Galerkin method

Details

Title: Subtitle: Numerical Analysis of Stochastic Elliptic Variational Inequalities of the First Kind
Creators: Chenhui Zhu - Xi'an Jiaotong University
Fei Wang - Xi'an Jiaotong University
Weimin Han - University of Iowa
Resource Type: Journal article
Publication Details: Journal of computational and applied mathematics, Vol.490, 117950
DOI: 10.1016/j.cam.2026.117950
ISSN: 0377-0427
eISSN: 1879-1778
Publisher: Elsevier B.V
Grant note: National Natural Science Foundation of China: 12171383 Simons Foundation Collaboration Grants: 850737
The work of F. Wang was partially supported by the National Natural Science Foundation of China (Grant No. 12171383) . The work of W. Han was partially supported by Simons Foundation Collaboration Grants (Grant No. 850737) .
Language: English
Electronic publication date: 07/14/2026
Date published: 01/15/2027
Academic Unit: Mathematics
Record Identifier: 9985183417102771

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