PPR Gradient Recovery For Elliptic Problems With Robin Boundary Condition

The finite element recovery techniques and its superconvergence property are con-sidered.For the application of posteriori error estimators based on the polynomial preserving recovery(PPR)in adaptive finite element methods,the superconvergence property of PPR catches a lot of attentions in both the academic world and the industri-al world.The well known superconvergence results are established with the Dirichlet boundary problem as its model,We consider the Robin boundary problem and analyze the superconvergence property of PPR under mildly structured meshes.Considering the linear finite element solution uh of the second-order elliptic e-quation with the Robin boundary condition,we prove that the PPR recovered gradient Ghuh has a superconvergence result ?hGuh-?u?L2(?)= O(h1+?+h2| lnh|1/2)under mildly structured triangular meshes,where the 0<p<1 is relating to the structural-ized degree of the mesh.We also compare two different strategies based on PPR for the gradient recovery of nodes on the boundary,which shows tiny difference between the superconvergence efficiency of these two.At the end,several numerical examples are given to test the theoretical results.