We develop a numerical method for the Westervelt equation, an important equation in nonlinear acoustics, in the form where the attenuation is represented by a class of non-local in time operators. A semi-discretisation in time based on the trapezoidal rule and A-stable convolution quadrature is stated and analysed. Existence and regularity analysis of the continuous equations informs the stability and error analysis of the semi-discrete system. The error analysis includes the consideration of the singularity at t = 0 which is addressed by the use of a correction in the numerical scheme. Extensive numerical experiments confirm the theory.
|Publication status||Published - 28 Oct 2022|
- 35L77, 65M06, 65M15, 35R11