Pointwise Superconvergence Patch Recovery for the Gradient of the Linear Tetrahedral Element.

We consider the finite element approximation to the solution of a self-adjoint, second-order elliptic boundary value problem in three dimensions over a fully uniform mesh of piecewise linear tetrahedral elements. First, the supercloseness of the gradients between the piecewise linear finite element solution uh and the linear interpolation uI is derived by using a weak estimate and an estimate of the discrete derivative Green's function. We then analyze a superconvergence patch recovery scheme for the gradient of the finite element solution, showing that the recovered gradient of uh is superconvergent to the gradient of the true solution u. [ABSTRACT FROM AUTHOR]