A graded mesh refinement approach for boundary layer originated singularly perturbed time‐delayed parabolic convection diffusion problems
In this work, we consider a graded mesh refinement algorithm for solving time‐delayed parabolic partial differential equations with a small diffusion parameter. The presence of this parameter leads to boundary layer phenomena. These problems are also known as singularly perturbed problems. For these...
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| Published in | Mathematical methods in the applied sciences Vol. 44; no. 16; pp. 12332 - 12350 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Freiburg
Wiley Subscription Services, Inc
15.11.2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0170-4214 1099-1476 |
| DOI | 10.1002/mma.7358 |
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| Abstract | In this work, we consider a graded mesh refinement algorithm for solving time‐delayed parabolic partial differential equations with a small diffusion parameter. The presence of this parameter leads to boundary layer phenomena. These problems are also known as singularly perturbed problems. For these problems, it is well‐known that one cannot achieve a convergent solution to maintain the boundary layer dynamics, on a fixed number of uniform meshes irrespective of the arbitrary magnitude of perturbation parameter. Here, we consider an adaptive graded mesh generation algorithm, which is based on an entropy function in conjunction with the classical difference schemes, to resolve the layer behavior. The advantage of the present algorithm is that it does not require to have any information about the location of the layer. Several examples are presented to show the high performance of the proposed algorithm. |
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| AbstractList | In this work, we consider a graded mesh refinement algorithm for solving time‐delayed parabolic partial differential equations with a small diffusion parameter. The presence of this parameter leads to boundary layer phenomena. These problems are also known as singularly perturbed problems. For these problems, it is well‐known that one cannot achieve a convergent solution to maintain the boundary layer dynamics, on a fixed number of uniform meshes irrespective of the arbitrary magnitude of perturbation parameter. Here, we consider an adaptive graded mesh generation algorithm, which is based on an entropy function in conjunction with the classical difference schemes, to resolve the layer behavior. The advantage of the present algorithm is that it does not require to have any information about the location of the layer. Several examples are presented to show the high performance of the proposed algorithm. |
| Author | Kumar, Kamalesh Das, Pratibhamoy Ramos, Higinio Podila, Pramod Chakravarthy |
| Author_xml | – sequence: 1 givenname: Kamalesh orcidid: 0000-0002-2527-3836 surname: Kumar fullname: Kumar, Kamalesh organization: Visvesvaraya National Institute of Technology – sequence: 2 givenname: Pramod Chakravarthy orcidid: 0000-0002-5540-6302 surname: Podila fullname: Podila, Pramod Chakravarthy organization: Visvesvaraya National Institute of Technology – sequence: 3 givenname: Pratibhamoy orcidid: 0000-0001-5095-0360 surname: Das fullname: Das, Pratibhamoy email: pratibhamoy@iitp.ac.in organization: Indian Institute of Technology – sequence: 4 givenname: Higinio orcidid: 0000-0003-2791-6230 surname: Ramos fullname: Ramos, Higinio organization: Universidad de Salamanca |
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| SubjectTerms | adaptive mesh algorithm algorithmic complexity Algorithms boundary layer phenomena Boundary layers Diffusion layers entropy graded mesh Grid refinement (mathematics) Mesh generation parabolic convection–diffusion problems Parabolic differential equations Parameters Partial differential equations Perturbation time delay |
| Title | A graded mesh refinement approach for boundary layer originated singularly perturbed time‐delayed parabolic convection diffusion problems |
| URI | https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fmma.7358 https://www.proquest.com/docview/2579207006 |
| Volume | 44 |
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