  In the present study, the zero- and first-order radiative correction to the
Casimir energy for the massive and massless scalar field confined with mixed
(Neumann-Dirichlet) boundary condition between two parallel lines in 2+1
dimensions for the self-interacting $\phi^4$ theory was computed. The main
point in this study is the use of a special program to renormalize the bare
parameters of the Lagrangian. The counterterm used in the renormalization
program, which was obtained systematically position-dependent, is consistent
with the boundary condition imposed on the quantum field. To regularize and
remove infinities in the calculation process of the Casimir energy, the Box
Subtraction Scheme as a regularization technique was used. In this scheme, two
similar configurations are usually introduced, and the vacuum energies of these
two configurations in proper limits are subtracted from each other. The final
answer for the problem is finite and consistent with the expected physical
basis. We also compared the new result of this paper to the previously reported
results in the zero- and first-order radiative correction to the Casimir energy
of scalar field in two spatial dimensions with Periodic, Dirichlet, and Neumann
boundary conditions. Finally, all aspects of this comparison were discussed.
