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

Wenya Qi

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

Numerical Analysis 2018-12-04 v1

Authors: Wenya Qi

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 $\theta$ -schemes in time for $\frac{1}{2}\leq\theta\leq 1$ , which include first-order backward Euler and second-order Crank-Nicolson schemes. Moreover, the optimal convergence rates in the $L^2$ and energy norms are derived. Numerical example is given to verify the theory.

Keywords

weak galerkin finite element methods galerkin methods discontinuous galerkin methods

Cite

@article{arxiv.1812.00601,
  title  = {A Weak Galerkin Method with Implicit $\theta$-schemes for Second-Order Parabolic Problems},
  author = {Wenya Qi},
  journal= {arXiv preprint arXiv:1812.00601},
  year   = {2018}
}

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