Analysis of one-dimensional Helmholtz equation with PML boundary

In this paper, the linear conforming finite element method for the one-dimensional Bérengerʹs PML boundary is investigated and well-posedness of the given equation is discussed. Furthermore, optimal error estimates and stability in the L 2 or H 1 -norm are derived under the assumption that h , h 2 ω 2 and h 2 ω 3 are sufficiently small, where h is the mesh size and ω denotes a fixed frequency. Numerical examples are presented to validate the theoretical error bounds.