ABSTRACT: We consider the construction of multiplier spaces for use with the mortar finite element method in three spatial dimensions in this paper. Some abstract conditions are given for the multiplier spaces which are sufficient to guarantee a stable and convergent mortar approximation. Three examples of multipliers satisfying these conditions are given. The first one is a dual basis example while the remaining two are based on finite volumes. Finally, the results of computational examples illustrating the theory are reported.
ACKNOWLEGEMENTS: This work was supported by the National Science Foundation under grant DMS~9973328, the Environmental Protection Agency under grant R~825207 and the State of Texas under ARP/ATP grant 010366-168. The work of the last author was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.