A Weak Galerkin Method with Implicit θ-schemes for Second-Order Parabolic Problems

2018/12/03 by Wenya Qi, Qi, Wenya
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1812.00601

openalex publication_date 2018/12/03 · openalex created_date 2018/12/11 · openalex updated_date 2026/08/01

Abstract

We introduce a new weak Galerkin finite element method whose weak functions on interior neighboring edges are double-valued for parabolic problems. Based on (P_k(T), P_k(e), RT_k(T)) element, a fully discrete approach is formulated with implicit θ-schemes in time for (1)/(2)≤θ≤ 1, which include first-order backward Euler and second-order Crank-Nicolson schemes. Moreover, the optimal convergence rates in the L² and energy norms are derived. Numerical example is given to verify the theory.

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