Superconvergence analysis for the explicit polynomial recovery method

A new recovery technique explicit polynomial recovery (EPR) is analyzed for finite element methods. EPR reconstructs the value at edge centers by solving a local problem. In combination with the finite element solution at the vertex, a quadratic approximation is constructed. Besides improving the accuracy, it can also be applied in building the EPR-based error estimator. For the Poisson equation, the element center is a superconvergent point of the gradient of the EPR recovered function on an equilateral triangulation. Numerical examples are presented to verify the theoretical results and to show the performance of the EPR in the adaptive finite element method.