Histotripsy with nonlinear ultrasound is an emerging noninvasive therapeutic modality that generates cavitation with high-intensity shock waves to precisely destroy diseased soft tissue. Numerical simulation of these shock waves in nonlinear, absorbing media is needed to characterize histotripsy systems and optimize treatments. We are developing a discontinuous Galerkin code based on the Westervelt equation to simulate transient wave propagation in the brain and skull. The discontinuous Galerkin method is a good choice for this simulation problem since this approach has high-order accuracy, geometric flexibility, low dispersion error, and excellent scalability on massively parallel machines. The Westervelt equation is formulated in a first-order flux form and discretized using a strong form of the discontinuous Galerkin method. Numerical results, both linear and nonlinear, from 1D and 2D discontinuous Galerkin codes, are presented and compared to both analytical and numerical benchmark solutions. In particular, the discontinuous Galerkin method captures nonlinear steepening of a high-intensity pulse with minimal numerical artifacts. The development of a 3D massively parallel code is also briefly discussed. [This work was supported in part by a grant from the Focused Ultrasound Foundation.]