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.
Wavenumber explicit convergence analysis for Galerkin discretizations of the Helmholtz equation.SIAM Journal on Numerical Analysis, 49(3):1210–1243
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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.