Abstract
In this paper, we present and study a stabilizer-free weak Galerkin (SFWG) finite element method for the Ciarlet-Raviart mixed form of the biharmonic equation on general polygonal meshes. We utilize the SFWG solutions of the second order elliptic problem to define projection operators and build error equations. Further, using weak functions formed by discontinuous k-th order polynomials, we derive the O(hk) convergence rate for the exact solution u in the H1 norm and the O(hk+1) convergence rate in the L2 norm. Finally, numerical examples support the results reached by the theory.
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