Abstract
We examine a time dependent singularly perturbed convection-diffusion problem, where the convective coefficient contains an interior layer. A smooth transformation is introduced to align the grid to the location of the interior layer. A numerical method consisting of an upwinded finite difference operator and a piecewise-uniform Shishkin mesh is constructed in this transformed domain. Numerical results are presented which indicate that the numerical approximations converge at a rate of first order (up to logarithmic factors) uniformly in the pointwise maximum norm.
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Dunne, R.K., O’ Riordan, E.: Interior layers arising in linear singularly perturbed differential equations with discontinuous coefficients. In: Farago, I., Vabishchevich P., Vulkov, L. (eds.) Proceedings of Fourth International Conference on Finite Difference Methods: Theory and Applications, pp. 29–38. Rousse University, Bulgaria (2007)
Dunne, R.K., O’ Riordan, E., Shishkin, G.I.: A fitted mesh method for a class of singularly perturbed parabolic problems with a boundary turning point. Comput. Methods Appl. Math. 3(3), 361–372 (2003)
Farrell, P.A., Hegarty, A.F., Miller, J.J.H., O’ Riordan, E., Shishkin, G.I.: Robust Computational Techniques for Boundary Layers. CRC, Boca Raton (2000)
Gracia, J.L., O’ Riordan, E.: A singularly perturbed convection–diffusion problem with a moving interior layer. Int. J. Numer. Anal. Model. 9(4), 823–843 (2012)
Ladyzhenskaya, O.A., Solonnikov, V.A., Ural’tseva, N.N.: Linear and Quasilinear Equations of Parabolic Type. Transactions of Mathematical Monographs, vol. 23. American Mathematical Society, Providence (1968)
O’ Riordan, E., Quinn, J.: A linearized singularly perturbed convection–diffusion problem with an interior layer. Appl. Numer. Math. 98, 1–17 (2015)
O’ Riordan, E., Shishkin, G.I.: Singularly perturbed parabolic problems with non-smooth data. J. Comput. Appl. Math. 166(1), 233–245 (2004)
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O’Riordan, E., Quinn, J. (2015). Numerical Experiments with a Linear Convection–Diffusion Problem Containing a Time-Varying Interior Layer. In: Knobloch, P. (eds) Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014. Lecture Notes in Computational Science and Engineering, vol 108. Springer, Cham. https://doi.org/10.1007/978-3-319-25727-3_17
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DOI: https://doi.org/10.1007/978-3-319-25727-3_17
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