Optimal order of uniform convergence for finite element method on Bakhvalov-type meshes
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We propose a new analysis of convergence for a kth order (k> 1) finite element method, which is applied on Bakhvalov-type meshes to a singularly perturbed two-point boundary value problem. A novel interpolant is introduced, which has a simple structure and is easy to generalize. By means of this interpolant, we prove an optimal order of uniform convergence with respect to the perturbation parameter. Numerical experiments illustrate these theoretical results.
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