Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
We investigate and analyze the grid convergence issues for an adaptive mesh refinement (AMR) code. These issues are related to the RAGE code, and have been raised in a previous report, ``Two-dimensional convergence study for problems with exact solution: uniform and adaptive grids'' (LA-UR-05-7985). We propose several methods to solve these issues. In particular, we propose and test a new mesh initialization for AMR solutions, and several refinement criteria to achieve the expected accuracy and convergence rate for AMR simulations. Three examples with exact solutions are used as model problems. Numerical experiments demonstrate the effectiveness of the proposed methods.
