The stochastic Galerkin method with linear finite elements for the stochastic obstacle problem achieves O(h) convergence in the H1-norm for expectation and second-moment errors.
Øksendal,Stochastic Differential Equations: An Introduction with Applications, Sixth Edition, Springer, Berlin; Heidelberg
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Numerical Analysis of Stochastic Elliptic Variational Inequalities of the First Kind
The stochastic Galerkin method with linear finite elements for the stochastic obstacle problem achieves O(h) convergence in the H1-norm for expectation and second-moment errors.