  We present a new high-order accurate spectral element solution to the
two-dimensional scalar Poisson equation subject to a general Robin boundary
condition. The solution is based on a simplified version of the shifted
boundary method employing a continuous arbitrary order $hp$-Galerkin spectral
element method as the numerical discretization procedure. The simplification
relies on a polynomial correction to avoid explicitly evaluating high-order
partial derivatives from the Taylor series expansion, which traditionally have
been used within the shifted boundary method. In this setting, we apply an
extrapolation and novel interpolation approach to project the basis functions
from the true domain onto the approximate surrogate domain. The resulting
solution provides a method that naturally incorporates curved geometrical
features of the domain, overcomes complex and cumbersome mesh generation, and
avoids problems with small-cut-cells. Dirichlet, Neumann, and general Robin
boundary conditions are enforced weakly through: i) a generalized Nitsche's
method and ii) a generalized Aubin's method. For this, a consistent asymptotic
preserving formulation of the embedded Robin formulations is presented.
  We present several numerical experiments and analysis of the algorithmic
properties of the different weak formulations. With this, we include
convergence studies under polynomial, $p$, increase of the basis functions,
mesh, $h$, refinement, and matrix conditioning to highlight the spectral and
algebraic convergence features, respectively. This is done to assess the
influence of errors across variational formulations, polynomial order, mesh
size, and mappings between the true and surrogate boundaries.
