Adaptive WENO Schemes for Singular in Space and Time Solutions of Nonlinear Degenerate Reaction-Diffusion Problems
The numerical solution of nonlinear degenerate reaction-diffusion problems often meets two kinds of difculties: singularities in space – finite speed of propagation of compact supports’ initial perturbations and possible sharp moving fronts, where the solution has low regularity, and singularities i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2016-01-01
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| Series: | EPJ Web of Conferences |
| Online Access: | http://dx.doi.org/10.1051/epjconf/201610802019 |
| Summary: | The numerical solution of nonlinear degenerate reaction-diffusion problems often meets two kinds of difculties: singularities in space – finite speed of propagation
of compact supports’ initial perturbations and possible sharp moving fronts, where the solution has low regularity, and singularities in time – blow-up or quenching in finite time. We propose and implement a combination of the sixth-order WENO scheme of Liu, Shu and Zhang [SIAM J.Sci.Comput. 33, 939–965 (2011)] with an adaptive procedure to deal with these singularities. Numerical results on the mathematical model of heat structures are shown. |
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| ISSN: | 2100-014X |