The Partition of Unity
نویسنده
چکیده
A new nite element method is presented that features the ability to include in the nite element space knowledge about the partial diierential equation being solved. This new method can therefore be more eecient than the usual nite element methods. An additional feature of the partition-of-unity method is that nite element spaces of any desired regularity can be constructed very easily. This paper includes a convergence proof of this method and illustrates its eeciency by an application to the Helmholtz equation for high wave numbers. The basic estimates for a-posteriori error estimation for this new method are also proved.
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