Chapter 9: Multiple-Interval Pseudospectral Methods and Adaptive Meshes
Local spectral accuracy, sparse global assembly, and adaptive hp refinement
Global pseudospectral approximations are exceptionally accurate for smooth solutions but can struggle near switches, boundary layers, or localized high curvature. The final chapter resolves that limitation by dividing the horizon into polynomial mesh intervals. It develops the local method, assembles the global sparse transcription, and then uses error estimates to decide where intervals should be split or polynomial degree increased.