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 H1 and L2 norms are established. Numerical tests are performed and reported. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013
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