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.
Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?SIAM Journal on Numerical Analysis, 34(6):2392–2423
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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.