2022/01/20 by Peng Zhu, Zhu, Peng, Shenglan Xie +3 · 1 citation
Engineering · Mathematics · #65N15 #65N30 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2201.08062
openalex publication_date 2022/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we present and analyze a stabilizer-free C0 weak Galerkin (SF-C0WG) method for solving the biharmonic problem. The SF-C0WG method is formulated in terms of cell unknowns which are C0 continuous piecewise polynomials of degree k+2 with k≥ 0 and in terms of face unknowns which are discontinuous piecewise polynomials of degree k+1. The formulation of this SF-C0WG method is without the stabilized or penalty term and is as simple as the C1 conforming finite element scheme of the biharmonic problem. Optimal order error estimates in a discrete H2-like norm and the H1 norm for k≥ 0 are established for the corresponding WG finite element solutions. Error estimates in the L2 norm are also derived with an optimal order of convergence for k>0 and sub-optimal order of convergence for k=0. Numerical experiments are shown to confirm the theoretical results.