A-posteriori error estimation in maximum norm for a strongly coupled system of two singularly perturbed convection–diffusion problems
A system of two singularly perturbed convection–diffusion problems with strong coupling is studied. This system is discretized by an upwind finite difference scheme on an arbitrary non-uniform mesh. An a posteriori error estimation in the maximum norm is derived. Based on the a posteriori error esti...
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| Published in | Journal of computational and applied mathematics Vol. 313; pp. 152 - 167 |
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| Format | Journal Article |
| Language | English |
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Elsevier B.V
15.03.2017
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| ISSN | 0377-0427 1879-1778 |
| DOI | 10.1016/j.cam.2016.08.020 |
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| Abstract | A system of two singularly perturbed convection–diffusion problems with strong coupling is studied. This system is discretized by an upwind finite difference scheme on an arbitrary non-uniform mesh. An a posteriori error estimation in the maximum norm is derived. Based on the a posteriori error estimation, a monitor function is proposed to design an adaptive grid algorithm. Especially, to implement the adaptive grid approach, we not only give a mesh generation algorithm, but also give a sub-algorithm, which is called an arc-length equidistribution algorithm. Numerical results are given to confirm our theoretical result.
•A maximum norm a posteriori error estimation is presented.•A monitor function is proposed to design an adaptive grid algorithm.•We give a sub-algorithm, which is called an arc-length equidistribution algorithm. |
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| AbstractList | A system of two singularly perturbed convection–diffusion problems with strong coupling is studied. This system is discretized by an upwind finite difference scheme on an arbitrary non-uniform mesh. An a posteriori error estimation in the maximum norm is derived. Based on the a posteriori error estimation, a monitor function is proposed to design an adaptive grid algorithm. Especially, to implement the adaptive grid approach, we not only give a mesh generation algorithm, but also give a sub-algorithm, which is called an arc-length equidistribution algorithm. Numerical results are given to confirm our theoretical result.
•A maximum norm a posteriori error estimation is presented.•A monitor function is proposed to design an adaptive grid algorithm.•We give a sub-algorithm, which is called an arc-length equidistribution algorithm. A system of two singularly perturbed convection-diffusion problems with strong coupling is studied. This system is discretized by an upwind finite difference scheme on an arbitrary non-uniform mesh. An a posteriori error estimation in the maximum norm is derived. Based on the a posteriori error estimation, a monitor function is proposed to design an adaptive grid algorithm. Especially, to implement the adaptive grid approach, we not only give a mesh generation algorithm, but also give a sub-algorithm, which is called an arc-length equidistribution algorithm. Numerical results are given to confirm our theoretical result. |
| Author | Liu, Li-Bin Chen, Yanping |
| Author_xml | – sequence: 1 givenname: Li-Bin surname: Liu fullname: Liu, Li-Bin organization: College of Mathematics and Statistics, Guangxi Teachers Education University, Nanning, 530001, China – sequence: 2 givenname: Yanping orcidid: 0000-0002-7765-8201 surname: Chen fullname: Chen, Yanping email: yanpingchen@scnu.edu.cn organization: School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China |
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| Cites_doi | 10.1093/imanum/21.1.349 10.1137/S003614290138471X 10.1137/1026104 10.1137/S1064827592234120 10.1093/imanum/19.2.233 10.1137/S0036142999355957 10.1137/S0036142900368642 10.1007/s10915-013-9814-9 10.1007/s10444-007-9058-z 10.1137/070683970 10.1007/s00607-006-0215-x 10.1016/j.apnum.2004.05.006 10.1016/S0377-0427(03)00563-6 10.1007/s10444-004-7641-0 |
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| SubjectTerms | Adaptive algorithms Algorithms Convection–diffusion Error analysis Finite difference method Mathematical analysis Mathematical models Maximum norm Monitors Norms Singularly perturbed Strongly coupled |
| Title | A-posteriori error estimation in maximum norm for a strongly coupled system of two singularly perturbed convection–diffusion problems |
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