Analysis of one-dimensional Helmholtz equation with PML boundary

摘要

In this paper, the linear conforming finite element method for the one-dimensional Bérenger's PML boundary is investigated and well-posedness of the given equation is discussed. Furthermore, optimal error estimates and stability in the L2 or H1-norm are derived under the assumption that h, h2ω2 and h2ω3 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.