An adaptive grid method for a singularly perturbed convection-diffusion equation with a discontinuous convection coefficient

被引：1

作者：

Mai, Xiongfa ^{[1
]}

Zhu, Ciwen ^{[1
]}

Liu, Libin ^{[1
]}

机构：

[1] Nanning Normal Univ, Sch Math & Stat, Nanning 530100, Peoples R China

来源：

NETWORKS AND HETEROGENEOUS MEDIA | 2023年 / 18卷 / 04期

关键词：

singularly perturbed; discontinuous convection coefficient; adaptive grid algorithm; a posteriori error estimate; HYBRID DIFFERENCE SCHEME; MAXIMUM NORM; NUMERICAL-METHOD; SYSTEM; BOUNDARY;

D O I：

10.3934/nhm.2023067

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, an adaptive grid method is put forward to solve a singularly perturbed convection-diffusion problem with a discontinuous convection coefficient. First, this problem is discretized by using an upwind finite difference scheme on an arbitrary nonuniform grid except the fixed jump point. Then, a first-order maximum norm a posterior error estimate is derived. Further, based on this a posteriori error estimation and the mesh equidistribution principle, an adaptive grid generation algorithm is constructed. Finally, some numerical experiments are presented that support our theoretical estimate.

引用

页码：1528 / 1538

页数：11

共 50 条

[21] The local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem with characteristic and exponential layers
Cheng, Yao
Stynes, Martin
NUMERISCHE MATHEMATIK, 2023, 154 (1-2) : 283 - 318
[22] GROUND STATES OF SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATION WITH OSCILLATING COEFFICIENTS
Piatnitski, A.
Rybalko, A.
Rybalko, V.
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2014, 20 (04) : 1059 - 1077
[23] NIPG Method on Shishkin Mesh for Singularly Perturbed Convection-Diffusion Problem with Discontinuous Source Term
Ranjan, Kumar Rajeev
Gowrisankar, S.
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2023, 20 (02)
[24] A Numerical Scheme for Singularly Perturbed Delay Differential Equations of Convection-Diffusion Type on an Adaptive Grid
Chakravarthy, P. Pramod
Gupta, Trun
Rao, R. Nageshwar
MATHEMATICAL MODELLING AND ANALYSIS, 2018, 23 (04) : 686 - 698
[25] Numerical approximations to a singularly perturbed convection-diffusion problem with a discontinuous initial condition
J. L. Gracia
E. O’Riordan
Numerical Algorithms, 2021, 88 : 1851 - 1873
[26] Asymptotic approximations for a singularly perturbed convection-diffusion problem with discontinuous data in a sector
López, JL
Sinusía, EP
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 181 (01) : 1 - 23
[27] Numerical approximations to a singularly perturbed convection-diffusion problem with a discontinuous initial condition
Gracia, J. L.
O'Riordan, E.
NUMERICAL ALGORITHMS, 2021, 88 (04) : 1851 - 1873
[28] A robust adaptive method for singularly perturbed convection-diffusion problem with two small parameters
Wu, Yujiang
Zhang, Na
Yuan, Jinyun
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 66 (06) : 996 - 1009
[29] Multiscale Convection in One Dimensional Singularly Perturbed Convection-Diffusion Problems
O'Riordan, E.
Quinn, J.
NUMERICAL ANALYSIS AND ITS APPLICATIONS, NAA 2012, 2013, 8236 : 73 - 85
[30] A staggered discontinuous Galerkin method for the convection-diffusion equation
Chung, E.
Lee, C. S.
JOURNAL OF NUMERICAL MATHEMATICS, 2012, 20 (01) : 1 - 31

← 1 2 3 4 5 →