(1) Singularity Preserving Numerical Methods for Boundary Integral

Equations, (with Y. Xu) May 8, 1995-May 7,1996, NASA Langley,

$27,000.

(2) Structure-Compatible Nonlinear Heat Transfer Analysis,

Error Estimates, Order Adaptivity and Design Optimization, (Gene

Hou- Principal Investigator, Hideaki Kaneko- Co-Principal

Investigator), May 2000-May 2003, NASA Langley, $180,000.

(3.) Error-Analysis for Discontinuous Galerkin Method for

Parabolic Problems, May 2001-May 2004, NASA Langley, $45,000.

(4.) A Posteriori Error Analysis for Hierarchical Finite

Element Method for Heat Conduction in Multilayered Plates, June

2004- May, 2007, NASA Langley $75,000.