Abstract
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.
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Acknowledgements
This work was supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. LY19A010008) and National Natural Science Foundation of China (Grant No. 12071184).
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Zhu, P., Xie, S. & Wang, X. A stabilizer-free C0 weak Galerkin method for the biharmonic equations. Sci. China Math. 66, 627–646 (2023). https://doi.org/10.1007/s11425-021-1947-0
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DOI: https://doi.org/10.1007/s11425-021-1947-0