A new low-order non-conforming mixed finite-element scheme for second-order elliptic problems

Abstract

The main aim of this paper is to develop a new low-order non-conforming mixed finite-element method to solve the second-order elliptic problems on rectangular meshes. The convergence analysis is presented and the optimal error estimates are derived with the lowest regularity of the exact solution. Numerical results which coincide with our theoretical analysis show that this element indeed has very good convergence behaviour.

Keywords:

• non-conforming
• mixed finite element
• elliptic problems
• lowest regularity
• optimal error estimates

Acknowledgements

This project is supported by the National Natural Science Foundation of China (No. 10671184;10971203).