Cea's error estimate for strongly monotone variational inequalities

Abstract

Céa's approximation lemma is extended to variational inequalities which are defined by strongly monotone operators in closed convex subsets of linear normed spaces. This abstract error estimate is applied to the finite element discretization of a nonlinear elliptic two-sided obstacle problem providing an asymptotic error estimate for a smooth enough solution.

Keywords:

• Cea's lemma
• monotone operator
• variational inequality
• p-Laplacian
• obstacle problem
• finite element discretization

AMS:

• 65N15
• 65N30