Can a finite element method perform arbitrarily badly?

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 L2-norm and the nodal point errors converge arbitrarily slowly. With the L2-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.

• Type: Journal
• Year: 2000
• Where: MOC
• Authors: Ivo Babuska, John E. Osborn
• Keywords: Elliptic Boundary Value, Finite Element Approximations, MOC 2000, Nodal Point Errors