Functional A Posteriori Error Control for Conforming Mixed Approximations of Coercive Problems with Lower Order Terms

TL;DR

This paper develops functional a posteriori error estimates for conforming mixed approximations of coercive PDEs with lower order terms, providing precise error control in combined primal-dual norms.

Contribution

It introduces new error equalities and two-sided estimates that are free of constants for a class of coercive PDEs with mixed formulations.

Findings

Derivation of functional a posteriori error equalities

Constant free two-sided error estimates

Effective error measurement in combined primal-dual norms

Abstract

We derive functional a posteriori error equalities and constant free two sided estimates for certain types of partial differential equations. The error is measured in a combined norm which takes into account both the primal and dual variable.