Function and Curl Recovery for the Lowest Order Triangular Edge Element

For the lowest order triangular edge element, function and curl recovery methods are proposed to recover the finite element approximation and its curl onto the space of piecewise continuous functions by least-squares fitting. A superconvergence analysis is carried out on the uniform triangular mesh. Numerical experiments are provided to illustrate the superconvergence of the recovery methods and the performance of the corresponding recovery based a posteriori error estimators in adaptive computation.