Superconvergent derivative recovery for Lagrange triangular elements of degree p on unstructured grids

In this paper, we develop a postprocessing derivative recovery scheme for the finite element solution u(h) on general unstructured but shape regular triangulations. In the case of continuous piecewise polynomials of degree p >= 1, by applying the global L-2 projection (Q(h)) and a smoothing operator (S-h), the recovered pth derivatives (S(h)(m)Q(h)partial derivative(p)u(h)) superconverge to the exact derivatives (partial derivative(p)u). Based on this technique we are able to derive a local error indicator depending only on the geometry of corresponding element and the (p + 1)st derivatives approximated by partial derivative S(h)(m)Q(h)partial derivative(p)u(h). We provide several numerical examples illustrating the effectiveness of our schemes. We also observe that higher order elements are likely to require more conservative refinement strategies to create meshes corresponding to optimal orders of convergence.