Skip to main content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.


The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

An a posteriori Error Estimate for Scanning Electron Microscope Simulation with Adaptive Mesh Refinement



William F. Mitchell, John S. Villarrubia


The intensity variation in a scanning electron microscope is a complex function of sample topography and composition. Measurement accuracy is improved when an explicit accounting for the relationship between signal and measurand is made. Because the determinants of the signal are many, the theoretical understanding usually takes the form of a simulator. For samples with nonconducting regions that charge, one phase of the simulation is finite element analysis to compute the electric field. The size of the finite element mesh, and consequently computation time, can be reduced through the use of adaptive mesh refinement. We present a new a posteriori local error estimator and adaptive mesh refinement algorithm for the scanning electron microscope simulation. This error estimate is designed to minimize the error in the electron trajectories, rather than the energy norm of the error that traditional error estimators minimize. Using a test problem with a known exact solution, we show that the adaptive mesh can achieve the same error in electron trajectories as a carefully designed hand-graded mesh while using 3.5 times fewer vertices and 2.25 times less computation time.
Journal of Scientific Computing


adaptive mesh refinement, a posteriori error estimation, scanning electron microscope simulation, finite element analysis
Created July 8, 2019, Updated August 28, 2019