In this work we show an error estimate for a first order Gaussian beam at fold caustic, approximating time-harmonic waves governed by the Helmholtz equation. For caustic that study exact solution can be constructed using Airy functions and there are explicit formulae parameters. Via precise comparisons pointwise on is of O ( k − 5 / 6 ) where wave number in Helmholtz.

Abstract We provide a posteriori error estimates in the energy norm for temporal semi-discretisations of wave maps into spheres that are based on angular momentum formulation. Our analysis is novel weak–strong stability which we combine with suitable reconstructions numerical solution. present time-adaptive simulations estimators solutions involving blow-up.