LOCAL ERROR ESTIMATES AND ADAPTIVE REFINEMENT FOR FIRST-ORDER SYSTEM LEAST SQUARES (FOSLS)

Abstract

. We establish an a-posteriori error estimate, with corresponding bounds, that is valid for any FOSLS L 2 -minimization problem. We present some numerical examples to support our theoretical results. We also establish a local lower a-priori error estimate, and present a theorem regarding error reduction for adaptive algorithms for FOSLS minimization problems. Key words. adaptive mesh refinement, a-posteriori error estimates, first-order system leastsquares AMS subject classifications. 65N15, 65N30, 65N50 1. Introduction. There has been substantial research recently in the field of first-order system least-squares methods (cf. [5], [7], [8], [6], [3], [4] and [11]). Most of the numerical examples presented in these papers are based on uniform grid implementations. However, in [11], the contribution that an element makes to the total value of the FOSLS functional is used as a local a-posteriori error estimate in a refinement process. This had been suggested earlier by a number of a...