ERROR EQUIDISTRIBUTION AND MESH ADAPTATION

The author reviews a number of strategies on mesh adaptation from a mathematical point of view and compares their performances in solving nonlinear diffusion models from semiconductor process modeling. Some new strategies are then proposed that improve on the existing ones. The analysis of the strategies based on monitoring interpolation errors and local truncation errors leads to a new theory on error equidistribution. Several implementation methods for equidistributing an error monitor function are also reviewed and outstanding problems am highlighted.