Abstract
A new weak Galerkin (WG) finite element method is designed featuring in using the first order polynomial to approximate solution of biharmonic equation. The proposed P1 WG method achieves O(h) convergence in energy norm and O(h2) in L2 norm in solving the biharmonic equation. This is not possible for the traditional finite element method as the minimum polynomial degree is 2 in order to approximate the biharmonic equation. Numerical tests on various polygonal meshes verify the theory.
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