An iterative grid redistribution method for singular problems in multiple dimensions
The authors introduce an iterative grid redistribution method for solving partial differential equations in multiple dimensions and with singularities. The method is based on the variational approach. The key ingredient of such adaptative methods is the grid generation rule and whether it is possible to determine an optimal coordinate mapping. Numerical examples are given. For instance, the authors treat the nonlinear Schrödinger equation where solutions with multiple blowup points can be solved up to times very close to the blowup time.
scientific article; zbMATH DE number 1443371
scientific article