Abstract
In this paper, we apply the weak Galerkin (WG) finite element method to solve the singularly perturbed fourth-order boundary value problem in a 2D domain. A Shishkin mesh is used to ensure that the method exhibits uniform convergence, regardless of the singular perturbation parameter. Asymptotically optimal order error estimate in a H2 discrete norm is established for the corresponding WG solutions. Numerical tests are provided to verify the convergence theory.
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