In this article, a weak Galerkin finite element method for the Laplace equation using the harmonic polynomial space is proposed and analyzed. The idea of using the ${P_k}$-harmonic polynomial space instead of the full polynomial space ${P_k}$ is to use a much smaller number of basis functions to achieve the same accuracy when k ≥ 2. The optimal rate of convergence is derived in both H1 and L2 norms. Numerical experiments have been conducted to verify the theoretical error estimates. In addition, numerical comparisons of using the P2-harmonic polynomial space and using the standard P2 polynomial space are presented.
Ahmed Al-Taweel, Yinlin Dong, Saqib Hussain, Xiaoshen Wang
. A Weak Galerkin Harmonic Finite Element Method for Laplace Equation[J]. Communications on Applied Mathematics and Computation, 2021
, 3(3)
: 527
-544
.
DOI: 10.1007/s42967-020-00097-z
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