Moving Finite Elements in 2-D.

In this second year of effort, truly large-scale computing aspects of PDEs partial differential equations have been addressed. MFE moving finite element node movement properties of highly sheared fluid flows and shocks were studied. The following results were obtained 1 extremely large nodal savings were obtained by the MFE method in highly sheared shock examples 2 such ODE solvers as the Gear method require significant restructuring of their internal code logic in order to achieve improved time step and error-controlling policies in PDE applications 3 iterative linear solvers are required in order to accommodate large MFE grid meshes 4 a new iterative solver of linear systems was developed in order to attain large convergence rates in advection-diffusion equations with highly inhomogeneous mesh spacings, which cannot be solved satisfactorily with other existing linear solvers 5 first-generation regularization schemes resolved highly sheared flows and, although large grid aspect ratios were resolved successfully, new regularization functions which homogenize MFE grid cells should be developed in future work and 6 singularities which are frequently troublesome in cylindrical and spherical co-ordinates are eliminated naturally in MFE inner product formulations. Author