Dedication

To my family. iv Acknowledgements First, my deepest gratitude goes to my advisor Olof Widlund. I thank him profoundly for his direction, guidance, support and advice during four years. I would also like to thank the rest of my committee: Professors Berger, Good-man, O’Neil and Stadler. In addition, I also thank Dr. Clark Dohrmann of the SANDIA-Albuquerque laboratories for his help and comments throughout my re-search. Finally I thank my Alma Mater, Universidad de Costa Rica, for the support during my academic education at NYU. v Two domain decomposition methods for solving vector field problems posed in H(curl) and discretized with Nédélec finite elements are considered. These finit