Most numerical schemes are implemented on uniform grids. But often uniform grids, in an attempt to resolve finescale features, use a fine uniform mesh and over-resolve areas of the domain. Methods which use non-uniform grids usually maintain the same grid for all time steps. These algorithms require an a priori knowledge of the regions which need a smaller mesh size. There are two possible types of problems where these methods fail to provide an optimal grid. The first is when the area needing a smaller mesh is unknown before the computation. The second is when the area needing greater resolution moves throughout the domain. The method provided here will efficiently find the computational grid and adapt the grid so that the grid is always optimal.