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Erschienen in:
13.03.2020 | Original Research
Study of the NIPG method for two–parameter singular perturbation problems on several layer adapted grids
Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2020
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Abstract
In this paper, we apply the non-symmetric interior penalty Galerkin (NIPG) method to obtain the numerical solution of two-parameter singularly perturbed convection-diffusion-reaction boundary-value problems. In order to discretize the domain, here, we use the layer-adapted piecewise-uniform Shishkin mesh, the Bakhvalov mesh and the exponentially-graded mesh. We establish a superconvergence result of the NIPG method, that is, the proposed method is parameter-uniformly convergent with the order almost \((k+1)\) on the Shishkin mesh and \((k+1)\) on the Bakhvalov mesh and on the exponentially graded mesh in the energy norm, where k is the order of the polynomials. Numerical results comparing the three different types of meshes are presented at the end of the article supporting the theoretical error estimates.