## A geometric weighted elliptic grid regeneration method for 3D unstructured ALE hydrodynamics

The theory for an elliptic mesh generator is developed for use in the advection step of a 3D ALE algorithm. This mesh generator is derived by a variational principle for an unstrutured 3D grid using finite elements. An arbitrary weight function is introduced which is based on the geometric properties of the existing mesh. These geometric weights should allow for a smooth grid that retains the general shape of the original mesh.