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In the present study, the zero- and first-order radiative correction to theCasimir energy for the massive and massless scalar field confined with mixed(Neumann-Dirichlet) boundary condition between two parallel lines in 2+1dimensions for the self-interacting $\phi^4$ theory was computed. The mainpoint in this study is the use of a special program to renormalize the bareparameters of the Lagrangian. The counterterm used in the renormalizationprogram, which was obtained systematically position-dependent, is consistentwith the boundary condition imposed on the quantum field. To regularize andremove infinities in the calculation process of the Casimir energy, the BoxSubtraction Scheme as a regularization technique was used. In this scheme, twosimilar configurations are usually introduced, and the vacuum energies of thesetwo configurations in proper limits are subtracted from each other. The finalanswer for the problem is finite and consistent with the expected physicalbasis. We also compared the new result of this paper to the previously reportedresults in the zero- and first-order radiative correction to the Casimir energyof scalar field in two spatial dimensions with Periodic, Dirichlet, and Neumannboundary conditions. Finally, all aspects of this comparison were discussed.

Radiative Correction to The Casimir Energy with Mixed Boundary Condition in 2+1 Dimensions