In this paper, we propose the medius error estimates for the interior penalty virtual element method for the biharmonic equation in two dimensions. Because the virtual element used here is not \(C^0\) -continuous, we construct an enriching operator that maps the \(H^1\) -nonconforming virtual element functions to the \(H^2\) -conforming counterparts. With the assistance of the enriching operator, we acquire the upper bound on the error measured by a mesh-dependent norm. Then some residual-type terms in the upper bound are estimated by the bubble function techniques, which are sourced from the posteriori error analysis. Finally, we obtain the optimal error estimates under the minimal regularity condition of the weak solution. A numerical example on the L-shaped domain is shown to confirm the theoretical results.
