Adaptive mesh refinement

Summary

Adaptive mesh refinement makes a computational mesh finer only where the solution needs it, guided by the computed solution itself. In finite element methods it runs a loop: solve, estimate the error on each element, mark elements with large error, and refine them. For time-dependent hyperbolic problems, block-structured refinement in space and time was developed by Marsha Berger and Joseph Oliger. Adaptivity recovers optimal convergence rates for solutions with singularities, where uniform refinement is slow. See the definition.