A posteriori error estimation for non-conforming quadrilateral finite elements

We derive an a posteriori error estimator giving a computable upper bound on the error in the energy norm for finite element approximation using the non-conforming rotated Q1 finite element. It is shown that the estimator also gives a local lower bound up to a generic constant. The bounds do not require additional assumptions on the regularity of the true solution of the underlying elliptic problem and, the mesh is only required to be locally quasi- uniform and may consist of general, non-a±ne convex quadrilateral elements.