H. Chen, Q. Lin, V. V. Shaidurov, J. Zhou, “Error estimates for triangular and tetrahedral finite elements in combination with a trajectory approximation of the first derivatives for advection-diffusion equations”, Sib. Zh. Vychisl. Mat., 14:4 (2011), 425–442; Num. Anal. Appl., 4:4 (2011), 345

Sibirskii Zhurnal Vychislitel'noi Matematiki

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Sib. Zh. Vychisl. Mat.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Sibirskii Zhurnal Vychislitel'noi Matematiki, 2011, Volume 14, Number 4, Pages 425–442 (Mi sjvm452)

This article is cited in 15 scientific papers (total in 15 papers)

Error estimates for triangular and tetrahedral finite elements in combination with a trajectory approximation of the first derivatives for advection-diffusion equations

H. Chen^a, Q. Lin^b, V. V. Shaidurov^cd, J. Zhou^e

^a School of Mathematical Sciences, Xiamen University, Xiamen, China
^b LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
^c Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk
^d School of Mathematics and Systems Science, Beihang University, Beijing, China
^e School of Sciences, Hebei University of Technology, Tianjin, China

Full-text PDF (305 kB) Citations (15)

References:

PDF

HTML

Abstract: In this paper, a modified method of characteristics in combination with integral identities of triangular and tetrahedral linear elements is used to prove a uniform optimal-order error estimate which depends only on the initial data and right-hand side, but not on a scaling parameter

ε

$\varepsilon$ , for multi-dimensional time-dependent advection-diffusion equations.

Key words: modified method of characteristics, triangular linear element, tetrahedral linear element, integral identities, uniform error estimate.

Received: 21.10.2010
Revised: 03.03.2011

English version:
Numerical Analysis and Applications, 2011, Volume 4, Issue 4, Pages 345–362
DOI: https://doi.org/10.1134/S1995423911040070

Bibliographic databases:

Document Type: Article

UDC: 556.013

Language: Russian

Citation: H. Chen, Q. Lin, V. V. Shaidurov, J. Zhou, “Error estimates for triangular and tetrahedral finite elements in combination with a trajectory approximation of the first derivatives for advection-diffusion equations”, Sib. Zh. Vychisl. Mat., 14:4 (2011), 425–442; Num. Anal. Appl., 4:4 (2011), 345–362

Citation in format AMSBIB

\Bibitem{CheLinSha11}

\by H.~Chen, Q.~Lin, V.~V.~Shaidurov, J.~Zhou

\paper Error estimates for triangular and tetrahedral finite elements in combination with a~trajectory approximation of the first derivatives for advection-diffusion equations

\jour Sib. Zh. Vychisl. Mat.

\yr 2011

\vol 14

\issue 4

\pages 425--442

\mathnet{http://mi.mathnet.ru/sjvm452}

\transl

\jour Num. Anal. Appl.

\yr 2011

\vol 4

\issue 4

\pages 345--362

\crossref{https://doi.org/10.1134/S1995423911040070}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84155189740}

Linking options:

https://www.mathnet.ru/eng/sjvm452

https://www.mathnet.ru/eng/sjvm/v14/i4/p425

This publication is cited in the following 15 articles:

Shaidurov V.V., Vyatkin A.V., Kuchunova E.V., “Semi-Lagrangian Difference Approximations With Different Stability Requirements”, Russ. J. Numer. Anal. Math. Model, 33:2 (2018), 123–135
V. Shaydurov, A. Efremov, L. Gileva, AIP Conference Proceedings, 2025, 2018, 020004
E. Dementyeva, E. Karepova, V. Shaidurov, “The semi-Lagrangian method for the Navier–Stokes problem for an incompressible fluid”, Application of Mathematics in Technical and Natural Sciences, AIP Conf. Proc., 1895, ed. M. Todorov, Amer. Inst. Phys., 2017, UNSP 110001-1
V. Shaydurov, G. Shchepanovskaya, M. Yakubovich, “A mathematical model and a numerical algorithm for an asteroid-comet body in the Earth's atmosphere”, Numerical Analysis and Its Applications (NAA 2016), Lecture Notes in Computer Science, 10187, eds. I. Dimov, I. Farago, L. Vulkov, Springler, 2017, 119–131
V. Shaydurov, G. Shchepanovskaya, M. Yakubovich, “Mathematical model and numerical algorithm for aerodynamical flow”, Application of Mathematics in Technical and Natural Sciences (AMITANS'16), AIP Conf. Proc., 1773, ed. M. Todorov, Amer. Inst. Phys., 2016, 020006
E. Dementyeva, E. Karepova, V. Shaidurov, “The semi-Lagrangian approximation in the finite element method for the Navier–Stokes equations”, Application of Mathematics in Technical and Natural Sciences (AMITANS'15), AIP Conf. Proc., 1684, ed. M. Todorov, Amer. Inst. Phys., 2015, 090009
A. Efremov, E. Karepova, A. Vyatkin, “Some features of the CUDA implementation of the semi-Lagrangian method for the advection problem”, Application of Mathematics in Technical and Natural Sciences (AMITANS'15), AIP Conf. Proc., 1684, ed. M. Todorov, Amer. Inst. Phys., 2015, 090003
V. Shaydurov, T. Liu, G. Shchepanovskaya, M. Yakubovich, “A semi-Lagrangian approximation in the Navier–Stokes equations for the gas flow around a wedge”, Application of Mathematics in Technical and Natural Sciences (AMITANS'15), AIP Conf. Proc., 1684, ed. M. Todorov, Amer. Inst. Phys., 2015, 090011
V. Shaydurov, G. Shchepanovskaya, M. Yakubovich, “A mathematical model of the passage of an asteroid-comet body through the Earth's atmosphere”, Application of Mathematics in Technical and Natural Sciences (AMITANS'15), AIP Conf. Proc., 1684, ed. M. Todorov, Amer. Inst. Phys., 2015, 020003
V. Shaidurov, G. Shchepanovskaya, M. Yakubovich, “A semi-Lagrangian approach in the finite element method for the Navier–Stokes equations of viscous heat-conducting gas”, Application of Mathematics in Technical and Natural Sciences (AMITANS `14), AIP Conf. Proc., 1629, ed. M. Todorov, Amer. Inst. Phys., 2014, 19–31
E. Andreeva, A. Vyatkin, V. Shaidurov, “The semi-Lagrangian approximation in the finite element method for Navier–Stokes equations for a viscous incompressible fluid”, International Conference on Analysis and Applied Mathematics (ICAAM 2014), AIP Conf. Proc., 1611, eds. A. Ashyralyev, E. Malkowsky, Amer. Inst. Phys., 2014, 3–11
Alexander Efremov, Eugeniya Karepova, Vladimir Shaydurov, Alexander Vyatkin, “A Computational Realization of a Semi-Lagrangian Method for Solving the Advection Equation”, Journal of Applied Mathematics, 2014 (2014), 1
H. Chen, Q. Lin, J. Zhou, H. Wang, “Uniform error estimates for triangular finite element solutions of advection-diffusion equations”, Adv. Comput. Math., 38:1 (2013), 83–100
Vladimir V. Shaydurov, Galina I. Shchepanovskaya, Maxim V. Yakubovich, Lecture Notes in Computer Science, 8236, Numerical Analysis and Its Applications, 2013, 122
V. V. Shaidurov, G. I. Shchepanovskaya, V. M. Yakubovich, “Numerical simulation of supersonic flows in a channel”, Russ. J. Numer. Anal. Math. Model, 27:6 (2012), 585–601

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

Sibirskii Zhurnal Vychislitel'noi Matematiki

Statistics & downloads:
Abstract page:	421
Full-text PDF :	95
References:	61
First page:	3

Что такое QR-код?

Registration to the website

Logotypes