Istit. Lombardo Accad. Sci. Lett. Rend. A, 127 (1993), 67-82.
Ricardo H. Nochetto
Department of Mathematics
University of Maryland, College Park
College Park, MD 20742, USA
The a posteriori error estimator due to Bank and Weiser, for piecewise linear finite elements, is shown to be equivalent to the finite element error in the energy norm without requiring the so-called saturation assumption. Such an estimator is based on the solution of elementwise Neumann problems. The present result requires minimal regularity of the data and no a priori regularity of the exact solution. A scalar linear elliptic problem with variable coefficients over a polygon, possibly with slit boundary, is examined. The case of discontinuous coefficients is also studied.