Simultaneous Approximation in Scales of Banach Spaces

James H. Bramble, Ridgway Scott
1978 Mathematics of Computation  
The problem of verifying optimal approximation simultaneously in different norms in a Banach scale is reduced to verification of optimal approximation in the highest order norm. The basic tool used is the Banach space interpolation method developed by Lions and Peetre. Applications are given to several problems arising in the theory of finite element methods.
doi:10.2307/2006327 fatcat:sksxtg5eenbtbpxqhuj7xzprcy