Transport Error Estimates for Adaptive Refinement of Spatial Grids

摘要

For efficient numerical solution of integro-differential equations, researchers have long sought to "adapt" discretizations to a given problem's solution. Here we discuss adaptive refinement of the spatial grid to efficiently solve particle-transport problems discretized via Discontinuous Finite Element Methods (DFEMs). In particular, we study the effectiveness of two indicators of cellwise discretization error and also a new technique for estimating the actual solution error.