THE PARTITION OF UNITY METHOD

A new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differ ential equation being solved. This new method can therefore be more ef ficient than the usual finite element methods. An additional feature o f the partition-of-unity method is that finite element spaces of any d esired regularity can be constructed very easily. This paper includes a convergence proof of this method and illustrates its efficiency by a n application to the Helmholtz equation for high wave numbers. The bas ic estimates for a posteriori error estimation for this new method are also proved.