  Accurate triangulation of the domain plays a pivotal role in computing the
numerical approximation of the differential operators. A good triangulation is
the one which aids in reducing discretization errors. In a standard collocation
technique, the smooth curved domain is typically triangulated with a mesh by
taking points on the boundary to approximate them by polygons. However, such an
approach often leads to geometrical errors which directly affect the accuracy
of the numerical approximation. To restrict such geometrical errors,
\textit{isoparametric}, \textit{subparametric}, and \textit{iso-geometric}
methods were introduced which allow the approximation of the curved surfaces
(or curved line segments). In this paper, we present an efficient finite
element method to approximate the solution to the elliptic boundary value
problem (BVP), which governs the response of an elastic solid containing a
v-notch and inclusions. The algebraically nonlinear constitutive equation along
with the balance of linear momentum reduces to second-order quasi-linear
elliptic partial differential equation. Our approach allows us to represent the
complex curved boundaries by smooth \textit{one-of-its-kind} point
transformation. The main idea is to obtain higher-order shape functions which
enable us to accurately compute the entries in the finite element matrices and
vectors. A Picard-type linearization is utilized to handle the nonlinearities
in the governing differential equation. The numerical results for the test
cases show considerable improvement in the accuracy.
