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 Zh. Vychisl. Mat. Mat. Fiz., 1992, Volume 32, Number 4, Pages 550–566 (Mi zvmmf2911)

A difference approximation of a singularly perturbed boundary-value problem for quasilinear elliptic equations degenerating into first-order equations

G. I. Shishkin

Ekaterinburg

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English version:
Computational Mathematics and Mathematical Physics, 1992, 32:4, 467–480

Bibliographic databases:
UDC: 519.632
MSC: Primary 65N06; Secondary 65N12, 35J65, 35B25
Revised: 20.05.1991

Citation: G. I. Shishkin, “A difference approximation of a singularly perturbed boundary-value problem for quasilinear elliptic equations degenerating into first-order equations”, Zh. Vychisl. Mat. Mat. Fiz., 32:4 (1992), 550–566; Comput. Math. Math. Phys., 32:4 (1992), 467–480

Citation in format AMSBIB
\Bibitem{Shi92} \by G.~I.~Shishkin \paper A difference approximation of a singularly perturbed boundary-value problem for quasilinear elliptic equations degenerating into first-order equations \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 1992 \vol 32 \issue 4 \pages 550--566 \mathnet{http://mi.mathnet.ru/zvmmf2911} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1168684} \zmath{https://zbmath.org/?q=an:0808.65102} \transl \jour Comput. Math. Math. Phys. \yr 1992 \vol 32 \issue 4 \pages 467--480 \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992KV60300005} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. D. Liseǐkin, “A survey of methods for constructing structured adaptive grids”, Comput. Math. Math. Phys., 36:1 (1996), 1–32
2. G. I. Shishkin, “Grid approximations of singularly perturbed systems for parabolic convection-diffusion equations with counterflow”, Sib. zhurn. vychisl. matem., 1:3 (1998), 281–297
3. G. I. Shishkin, “Finite-difference approximations for singularly perturbed elliptic equations”, Comput. Math. Math. Phys., 38:12 (1998), 1909–1921
4. G. I. Shishkin, “A grid approximation for the Riemann problem in the case of the Burgers equation”, Comput. Math. Math. Phys., 38:8 (1998), 1361–1363
5. G. I. Shishkin, “Increasing the accuracy of approximate solutions by residual correction for singularly perturbed equations with convective terms”, Russian Math. (Iz. VUZ), 43:5 (1999), 77–89
6. G. I. Shishkin, “Singularly perturbed boundary value problems with locally perturbed initial conditions: Equations with convective terms”, Comput. Math. Math. Phys., 39:2 (1999), 249–265
7. G. I. Shishkin, “Grid approximation of singularly perturbed boundary value problems on locally condensing grids: Convection-diffusion equations”, Comput. Math. Math. Phys., 40:5 (2000), 680–691
8. Farrell P.A., Hegarty A.F., Miller J.J.H., O'Riordan E., Shishkin G.I., “Numerical techniques for flow problems with singularities”, International Journal For Numerical Methods in Fluids, 43:8 (2003), 915–936
9. Linss T., “Layer-adapted meshes for convection-diffusion problems”, Comput Methods Appl Mech Engrg, 192:9–10 (2003), 1061–1105
10. G. I. Shishkin, “The use of solutions on embedded grids for the approximation of singularly perturbed parabolic convection-diffusion equations on adapted grids”, Comput. Math. Math. Phys., 46:9 (2006), 1539–1559
11. Shishkin G.I., “Using the technique of majorant functions in approximation of a singular perturbed parabolic convection-diffusion equation on adaptive grids”, Russian Journal of Numerical Analysis and Mathematical Modelling, 22:3 (2007), 263–289
12. G. I. Shishkin, L. P. Shishkina, “A Richardson scheme of an increased order of accuracy for a semilinear singularly perturbed elliptic convection-diffusion equation”, Comput. Math. Math. Phys., 50:3 (2010), 437–456
13. Linss T., “Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems Introduction”, Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems, Lecture Notes in Mathematics, 1985, 2010, 1
14. Shishkin G.I., Shishkina L.P., “Iterative Newton solution method for the Richardson scheme for a semilinear singular perturbed elliptic convection-diffusion equation”, Russian J Numer Anal Math Modelling, 26:4 (2011), 427–445
15. Zh. O. Dombrovskaya, “Metod konechnykh raznostei vo vremennoi oblasti dlya kusochno-odnorodnykh dielektricheskikh sred”, Model. i analiz inform. sistem, 23:5 (2016), 539–547
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