A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem. (English) Zbl 1398.65186
Summary: We propose a continuous interior penalty finite element method designed for a third-order singularly perturbed problem. Using higher order polynomials on Shishkin-type layer-adapted meshes, a robust convergence has been proved in the corresponding energy norm. Moreover, we show numerical experiments which support our theoretical findings.
MSC:
| 65L11 | Numerical solution of singularly perturbed problems involving ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for 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 differential equation; third-order boundary value problem; interior penalty finite element method; layer-adapted meshReferences:
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