A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is
Can a finite element method perform arbitrarily badly?
Mathematics of Computation
In this paper we construct elliptic boundary value problems whose standard finite element approximations converge arbitrarily slowly in the energy norm, and show that adaptive procedures cannot improve this slow convergence. We also show that the L 2 -norm and the nodal point errors converge arbitrarily slowly. With the L 2 -norm two cases need to be distinguished, and the usual duality principle does not characterize the error completely. The constructed elliptic problems are one dimensional.doi:10.1090/s0025-5718-99-01085-6 fatcat:kxk2wk5jfbe4hllf77v7daciem