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The Kuznetsov equation is a classical wave model of acoustics thatincorporates quadratic gradient nonlinearities. When its strong dampingvanishes, it undergoes a singular behavior change, switching from aparabolic-like to a hyperbolic quasilinear evolution. In this work, weestablish for the first time the optimal error bounds for its finite elementapproximation as well as a semi-implicit fully discrete approximation that arerobust with respect to the vanishing damping parameter. The core of the newarguments lies in devising energy estimates directly for the error equationwhere one can more easily exploit the polynomial structure of thenonlinearities and compensate inverse estimates with smallness conditions onthe error. Numerical experiments are included to illustrate the theoreticalresults.

Robust fully discrete error bounds for the Kuznetsov equation in the inviscid limit