A posteriori error estimation for variational problems with uniformly convex functionals

The objective of this paper is to introduce a general scheme for deriving a posteriori error estimates by using duality theory of the calculus of variations. We consider variational problems of the form inf vV {F (v) + G(v)}, where F : V R is a convex lower semicontinuous functional, G : Y R is a uniformly convex functional, V and Y are reflexive Banach spaces, and : V Y is a bounded linear operator. We show that the main classes of a posteriori error estimates known in the literature follow from the duality error estimate obtained and, thus, can be justified via the duality theory.

• Type: Journal
• Year: 2000
• Where: MOC
• Authors: Sergey I. Repin
• Keywords: Duality Theory, General Scheme, MOC 2000, Posteriori Error