Weak Galerkin Finite Element Methods for Parabolic Equations
  A newly developed weak Galerkin method is proposed to solve parabolic equations. This method allows the usage of totally discontinuous functions in approximation space and preserves the energy conservation law. Both continuous and discontinuous time weak Galerkin finite element schemes are developed and analyzed. Optimal order error estimates in both H^1 and L^2 norms are established. Numerical tests are performed and reported. 
Qiaoluan H. Li and Junping Wang
math.NA