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We introduce a new weak Galerkin finite element method whose weak functionson interior neighboring edges are double-valued for parabolic problems. Basedon $(P_k(T), P_{k}(e), RT_k(T))$ element, a fully discrete approach isformulated with implicit $\theta$-schemes in time for$\frac{1}{2}\leq\theta\leq 1$, which include first-order backward Euler andsecond-order Crank-Nicolson schemes. Moreover, the optimal convergence rates inthe $L^2$ and energy norms are derived. Numerical example is given to verifythe theory.

A Weak Galerkin Method with Implicit $\theta$-schemes for Second-Order Parabolic Problems