NIPG finite element method for convection-dominated diffusion problems with discontinuous data. (English) Zbl 07714969
Summary: This paper presents the nonsymmetric interior penalty Galerkin (NIPG) finite element method for a class of one-dimensional convection dominated diffusion problems with discontinuous coefficients. The solution of the considered class of problem exhibits boundary and interior layers. Piecewise uniform Shishkin-type meshes are used for the spatial discretization. The error estimates in the energy norm have been derived for the proposed schemes. Theoretical results are supported by conducting numerical experiments. It is established that the errors are uniform with respect to the perturbation parameter \(\varepsilon\). The uniformness of the error estimates with the perturbation parameter \(\varepsilon\) has also been established numerically for \(L_\infty\)-norm.
MSC:
| 65L11 | Numerical solution of singularly perturbed problems involving ordinary differential equations |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
Keywords:
singularly perturbed problem; discontinuous data; interior layer; boundary layer; Shishkin mesh; discontinuous Galerkin finite element method; convection-diffusion problemsReferences:
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