Article information

2020 , Volume 25, 1, p.49-65

Liseikin V.D., Karasuljic S.

Numerical analysis of grid-clustering rules for problems with power of the first type boundary layers

This paper demonstrates results of numerical experiments on some popular and new layer-resolving grids applied for solving one-dimensional singularly-perturbed problems having power of the first type boundary layers.


Keywords: singularly perturbed equations, small parameter, boundary and interior layers, grid generation

doi: 10.25743/ICT.2020.25.1.004

Author(s):
Liseikin Vladimir Dmitrievich
Dr. , Professor
Position: Leading research officer
Office: Institute of Computational Technologies SB RAS
Address: 630090, Russia, Novosibirsk, pr. Lavrentjeva, 6
Phone Office: (383) 330 73 73
E-mail: lvd@ict.nsc.ru
SPIN-code: 5198

Karasuljic Samir
Dr. , Associate Professor
Position: Associate Professor
Office: University of Tuzla
Address: 75000, Bosnia and herzegovina, Tuzla, Univerzitetska br.4
Phone Office: (387) 35 320 902
E-mail: samir.karasuljic@gmail.com

References:

[1] Bakhvalov N.S. On the optimization of the methods for solving boundary value problems in the presence of a boundary layer. USSR Computational Mathematics and Mathematical Physics. 1969; 9(4):139166.

[2] Vulanovi´c R. Mesh construction for numerical solution of a type of singular perturbation problems. Numer. Meth. Approx. Theory; 1984:137142.

[3] Miller J.J.K., ORiordan E., Shishkin G.I. Fitted numerical methods for singular perturbation problems. Singapore, New Jersey, London, Hong Kong: World Scientific; 2012: 191.

[4] Roos H.-G., Stynes M., Tobiska L. Numerical methods for singularly perturbed differential equations. Convection-Diffusion and Flow Problems. New York: Springer; 2010: 604.

[5] Linss T. Layer-adapted meshes for reaction-convection-diffusion problems. Berlin: SpringerVerlag; 2010: 320.

[6] Liseikin V.D. Grid generation methods. Third ed. Berlin: Springer; 2017: 530.

[7] Liseikin V.D., Yanenko N.N. On the numerical solution of equations with interior and exterior layers on a nonuniform mesh. BAIL III. Proc. 3th Internarional Conference on Boundary and Interior Layers-Computational and Asymptotic Methods. 1984, Dublin, Ireland: Trinity College; 1984: 6880.

[8] Liseikin V.D. Numerical solution of equations with power boundary layer. USSR Computational Mathematics and Mathematical Physics. 1986; 26(6):133139.

[9] Liseikin V.D. On the numerical solution of singularly perturbed equations with a turning point. J. Comput. Maths. Math. Phys. 1984; 24(6):135139.

[10] Liseikin V.D. Grid generation for problems with boundary and interior layers. Novosibirsk: NGU; 2018: 296. (In Russ.)

[11] Polubarinova-Kochina, P.Ya. Theory of motion of phreatic water. Moscow: Nauka; 1977:665. (In Russ.)

[12] Liseikin V.D. Layer resolving grids and transformations for singular perturbation problems. Utrecht: VSP; 2001: 284.

[13] Becher S. FEM-analysis on graded meshes for turning point problems exhibiting an interior layer. 2016:117. Available at: https://arxiv.org/abs/1603.04653

[14] Liseikin V.D., Paasonen V.I. Compact difference schemes and layer-resolving grids for numerical modeling of problems with boundary and interior layers. Numerical Analysis and Applications. 2019; 12(1):117.

Bibliography link:
Liseikin V.D., Karasuljic S. Numerical analysis of grid-clustering rules for problems with power of the first type boundary layers // Computational technologies. 2020. V. 25. 1. P. 49-65
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