Local error estimates and adaptive refinement for first-order system least squares (FOSLS) (Q1381052)

This paper deals with the FOSLS methodology. The authors establish the theory for such a local a posteriori error estimate using only results from standard FOSLS theory in a general setting and prove that any FOSLS \(L^2\)-functional can be used as a local a posteriori estimate for error in the norm that it induces. Next, they show how the FOSLS functional can be used to obtain a local a priori lower error bound. Some numerical examples to support the theoretical results are presented.