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., 2011, Volume 14, Number 4,Pages <nobr>425

This article is cited 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

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 $\varepsilon$, 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.

UDC: 556.013

Received: 21.10.2010
Revised: 03.03.2011