  In this paper, we analyze convergence and supercloseness properties of a
class of weak Galerkin (WG) finite element methods for solving second-order
elliptic problems. It is shown that the WG solution is superclose to the
Lagrange type interpolation using Lobatto points. This supercloseness behavior
is obtained through some newly designed stabilization terms. A post-processing
technique using the polynomial preserving recovery (PPR) is introduced for WG
approximation. Superconvergence analysis is carried out for the PPR
approximation. Numerical examples are provided to verify our theoretical
results.
