Derives matching upper and lower bounds on absolute and relative discretization errors for centered FD on 1D Helmholtz via Fourier analysis under stated assumptions on k and h.
A sharp relative-error bound for the Helmholtz h-FEM at high frequency.Numerische Mathematik, 150(1):137–178, 2022
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Fourier Analysis of Finite Difference Schemes for the Helmholtz Equation in 1D with Dirichlet Conditions: Sharp Estimates and Relative Errors
Derives matching upper and lower bounds on absolute and relative discretization errors for centered FD on 1D Helmholtz via Fourier analysis under stated assumptions on k and h.