High-frequency, nonphysical oscillations introduced by numerical approximation that do not reflect the true solution, typically appearing near discontinuities, steep gradients, or unresolved features.

Principle

When a numerical scheme lacks sufficient dissipation, monotonicity or appropriate stabilization, numerical dispersion or Gibbs-type interference excites nonphysical high-frequency modes that persist or grow despite mesh refinement in certain norms.

Demonstration

A central-difference discretization of a linear advection equation with a sharp front produces oscillatory ripples downstream of the front; adding an upwind bias or a flux limiter removes or suppresses those oscillations.

Misapplication

Interpreting numerically observed oscillations as genuine small-scale physics (e.g., turbulence) without model validation; treating a spurious oscillation by indiscriminate smoothing can erase legitimate features.

Consequence

Spurious oscillations contaminate diagnostics, reduce convergence order in norms sensitive to high frequencies, and can destabilize iterative solvers; correcting them requires stabilization, limiters, filtering, or change of discretization.

Reversal

Replacing a nondissipative scheme with a monotone, TVD, or properly stabilized method suppresses spurious oscillations but may introduce numerical diffusion or smear sharp features.

Boundary

Occurs in discrete approximations of hyperbolic, advection-dominated, or spectral problems when stability/monotonicity conditions are violated; does not refer to physical high-frequency signals that are well-resolved and model-consistent.

Semantic Tension

Closely related to Gibbs phenomenon and to underresolution of true physics; the distinction is that spurious oscillations are artifacts of the numerical method rather than the limit behaviour of a convergent global series.

Synthesis

Spurious oscillation is a numerical artifact: nonphysical high-frequency structure produced when a discretization lacks the correct dissipative or monotonic properties, identifiable by its dependence on scheme and removable by stabilization or filtering.