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).
