Development of an error-minimizing adaptive grid method Original Research Article

We present the first step in the development of a moving adaptive grid technique for flow and transport problems that is based on the approximate minimization in the L1 norm of the modeling error due to discretization. The technique consists of a second-order accurate discretization scheme designed for error analysis, a filter technique to ensure sufficiently smooth solutions, and an iterative solver for the nonlinear adaptive grid equations. We describe how these elements have been used for the numerical approximation of a given one-dimensional function. This application has been chosen to test and optimize the error-minimizing adaptive grid method. Results are presented for a function having a smooth part, a discontinuity and a uniform part. In comparison with a uniform grid, a gain in accuracy of a factor 10 to almost 1000 was obtained using 40 to 200 grid points.