Weak Galerkin method with implicit θ-schemes for second-order parabolic problems

摘要

We introduce a new weak Galerkin finite element method whose weak functions on interior edges are double-valued and approximation spaces are based on (Pk(T), Pk(e), RTk(T)) elements. It is natural to develop a semi-discrete stable scheme for parabolic problems, and then fully discrete approaches are formulated with implicit θ-schemes in time for 1/2 ≤ θ ≤ 1, which include first-order backward Euler (θ=1) and second-order Crank-Nicolson schemes (θ=1/2). Furthermore, optimal convergence rates in the L2 and energy norms are derived. Numerical results are given to verify the theory.