1. [Untitled]
- Author
-
Robert C. Kirby
- Subjects
Mathematical optimization ,Scalar (mathematics) ,Mixed finite element method ,Residual ,Upper and lower bounds ,Computer Science Applications ,Computational Mathematics ,Boundary layer ,Variable (computer science) ,Singularity ,Computational Theory and Mathematics ,Applied mathematics ,A priori and a posteriori ,Computers in Earth Sciences ,Mathematics - Abstract
In this paper, residual-based 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.
- Published
- 2003