• adaptivity;
  • time integration;
  • verification;
  • finite element;
  • explicit;
  • compressible flow


We assess the spatial accuracy and performance of a mixed-order, explicit multi-stage method in which an inexpensive low-order scheme is used for the initial stages, and a more expensive high-order scheme is used for the final stage only. Compared with the use of a high-order scheme for all stages, we observe that the mixed-order scheme achieves comparable accuracy and convergence while providing a speed-up of a factor of two on mesh sizes of O(106 − 107) tetrahedron. For calculations with significant adaptive mesh refinement, a more modest speed-up of 30% is obtained. Published 2012. This article is a US Government work and is in the public domain in the USA.