AN OPTIMAL FINITE ELEMENT BASIS FOR SOLVING ELLIPTIC BOUNDARY VALUE PROBLEMS

In this work, we give an optimal finite element basis for solving the elliptic boundary value problems. Moreover, a comparison between this new finite element(NFE), classical finite element(FEM) and Schauder hierarchical methods(SHM) is given for an elliptic boundary value problem. The condition numbers are our criteria for optimality. We show that by this new finite element method, the condition number would be bounded independent of level, as the level increases. The bases of FEM are chosen such that the dimension of space is the same with the dimension of FEM and SHM spaces.