Poincaré–Friedrichs Inequalities for Piecewise H² Functions

Abstract

Poincaré–Friedrichs inequalities are derived for piecewise H ² functions on two dimensional domains. These inequalities can be applied to classical non-conforming finite element methods, mortar methods and discontinuous Galerkin methods.

Key Words:

• Poincaré–Friedrichs inequalities
• Piecewise H ² functions
• Non-conforming finite elements
• Mortar methods
• Discontinuous Galerkin methods

Mathematics Subject Classification:

• Primary 65N30
• Secondary 46E35

Acknowledgment

This work was supported in part by the National Science Foundation under Grant No. DMS-03-11790.