Abstract
For the numerical solution of time dependent PDEs which involve large solution variations, a variety of grid distribution methods based on equidistribution (in one dimension) or variational approach (in multiple dimensions) have been shown to gain significant improvements in accuracy and efficiency over conventional fixed mesh method. However, direct applications of many of those methods to PDEs with singular behavior (e.g. finite time blow up) often fail due to lack of control of the resulting mesh distribution. We introduce a new iterative grid redistribution method to handle the singular solutions. Our method requires little prior information of the singular solutions and can handle multiple singularities.