  This study focuses on numerically approximating solutions to the nonlinear
periodic Westervelt equation within bounded domains in $\mathbb{R}^d$, where $d
\in \{2,3\}$, with Robin boundary conditions. We establish the existence and
uniqueness of solutions in the linear and nonlinear case, emphasizing the
importance of small excitations for existence and uniqueness in the nonlinear
case. Adopting a multiharmonic formulation, we address the nonlinear
propagation's harmonic frequencies. An iteration scheme is devised and its
convergence under smallness conditions on the excitation is shown. We explore
numerical solution to the resulting system of Helmholtz equations, with a
conforming finite element method for its discretization. Using an
implementation of the devised methodology, we showcase how acoustic waves
propagate within nonlinear media. This study is supposed to enhance our
understanding of ultrasound propagation dynamics, crucial for obtaining
high-quality images from limited boundary measurements.
