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

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  • Qi, Wenya
  • Song, Lunji

Abstract

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.

Suggested Citation

  • Qi, Wenya & Song, Lunji, 2020. "Weak Galerkin method with implicit θ-schemes for second-order parabolic problems," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    • Handle: RePEc:eee:apmaco:v:366:y:2020:i:c:s0096300319307234
    DOI: 10.1016/j.amc.2019.124731
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    References listed on IDEAS

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    1. Zhang, Tie & Chen, Yanli, 2019. "An analysis of the weak Galerkin finite element method for convection–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 612-621.
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