  The potentially significant role of the surface of an elastic body in the
overall response of the continuum can be described using the mature theory of
surface elasticity. The objective of this contribution is to detail the finite
element approximation of the underlying governing equations (both in the volume
and on its surface) and their solution using the open-source finite element
library deal.II. The fully-nonlinear (geometric and material) setting is
considered. The nonlinear problem is solved using a Newton--Raphson procedure
wherein the tangent contributions from the volume and surface are computed
exactly. The finite element formulation is implemented within the total
Lagrangian framework and a Bubnov-Galerkin spatial discretization of the volume
and the surface employed. The surface is assumed material. A map between the
degrees of freedom on the surface and on the boundary of the volume is used to
allocate the contribution from the surface to the global system matrix and
residual vector. The deal.II library greatly facilitates the computation of the
various surface operators, allowing the numerical implementation to closely
match the theory developed in a companion paper. Key features of the theory and
the numerical implementation are elucidated using a series of benchmark example
problems. The full, documented source code is provided.
