Abstract
A weak Galerkin (WG) finite element method without stabilizers was introduced in Ye and Zhang (2020) on polytopal mesh. Then it was improved in Ye and Zhang (2021) with order one superconvergence. The goal of this paper is to develop a new stabilizer free WG method on polytopal mesh. This method has convergence rates two orders higher than the optimal convergence rates for the corresponding WG solution in both an energy norm and the L2 norm. The numerical examples are tested for low and high order elements in two and three dimensional spaces.
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