Local error estimation and adaptive remeshing scheme for least-squares mixed finite elements

Abstract

Following the theme of our previous work on least-squares finite elements [10,28], we describe an adaptive remeshing scheme using local residuals as the error indicator. This choice of indicator is natural (and exact at the element level!) in the norm associated with the corresponding least-squares statement. The remeshing strategy applied here involves mesh enrichment by point insertion in a Delaunay scheme. Several refined grids and error plots are included for a representative model elliptic boundary-value problem.