A stabilizer-free C^0 weak Galerkin method for the biharmonic equations
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In this article, we present and analyze a stabilizer-free C^0 weak Galerkin (SF-C0WG) method for solving the biharmonic problem. The SF-C0WG method is formulated in terms of cell unknowns which are C^0 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 C^1 conforming finite element scheme of the biharmonic problem. Optimal order error estimates in a discrete H^2-like norm and the H^1 norm for k≥ 0 are established for the corresponding WG finite element solutions. Error estimates in the L^2 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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