# TR-2003-06

## Residual a posteriori error estimates for the mixed finite element method

Robert C. Kirby. 28 March, 2003.
Communicated by Robert Kirby.

### Abstract

In this paper, residual-based {\em a posteriori} error bounds are derived for the mixed finite element method applied to a model second order elliptic problem. A global upper bound for the error in the scalar variable is established, as well as a local lower bound. In addition, due to the fact that the scalar and vector variables are approximated to equal order accuracy, the dual problem may be modified to give an upper bound for the vector variable. Some comments on estimating more general error quantities are also made. The estimate effectively guides adaptive refinement for a smooth problem with a boundary layer, as well as detects the need to refine near a singularity.

### Original Document

The original document is available in Postscript (uploaded 28 March, 2003 by Robert Kirby).