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Convergence of a finite element method on a Bakhvalov-type mesh for singularly perturbed reaction-diffusion equation. (English) Zbl 1508.65162

Summary: A finite element method is applied on a Bakhvalov-type mesh to solve a singularly perturbed reaction-diffusion problem whose solution exhibits boundary layers. A uniform convergence order of \(\mathcal{O} (N^{- (k+1)} + \varepsilon^{1/2} N^{- k})\) is proved, where \(k\) is the order of piecewise polynomials in the finite element method, \( \varepsilon\) is the diffusion parameter and \(N\) is the number of partitions in each direction. Numerical experiments support this theoretical result.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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