The stabilizer-free weak Galerkin finite element method for the Biharmonic equation using polynomials of reduced order

2024/01/25 by Gu, Shanshan, Zhai, Qilong
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2401.14163

Abstract

In this article, we decrease the degree of the polynomials on the boundary of the weak functions and modify the definition of the weak laplacian which are introduced in \citeBiharmonicSFWG to use the SFWG method for the biharmonic equation. Then we propose the relevant numerical format and obtain the optimal order of error estimates in H² and L² norms. Finally, we confirm the estimates using numerical experiments.

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