A perspective on adaptive modeling and meshing (AM&M)

The purpose of this study is to develop an integrated approach to adaptive modeling in conjunction with adaptive meshing. This involves consideration of the modeling error from various sources and the discretization error in the numerical scheme. Adapting the model to control error due to geometry, boundary data, constitutive relations and model parameters can be integrated with adaptive mesh control to improve numerical reliability. Other factors such as stabilization by artificial dissipation and regularization are considered. A class of hybrid algorithms are developed to combine these approaches.