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

Wenya Qi and Lunji Song

Applied Mathematics and Computation, 2020, vol. 366, issue C

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.

Keywords: Parabolic problem; Weak galerkin; Double-valued functions; Implicit θ-schemes; Error estimates (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:366:y:2020:i:c:s0096300319307234

DOI: 10.1016/j.amc.2019.124731

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