A posteriori error analysis of nonconforming finite-element discretization for the Stokes equations

Abstract

In this paper, we extend the unifying theory for a posteriori error analysis of the nonconforming finite-element methods to the Stokes problems. We present explicit residual-based computable error indicators, we prove its reliability and efficiency based on two assumptions concerning both the weak continuity and the weak orthogonality of the nonconforming finite-element spaces, respectively, and we apply the unified framework to various nonconforming finite elements from the literature.

Keywords:

• nonconforming finite element
• mixed finite element
• Helmholtz decomposition
• a posteriori error analysis
• Stokes equations

2000 AMS Subject Classifications :

• 65N30
• 65N15
• 35J25