Lifting solutions of quasilinear convection-dominated problems
In certain cases, quasilinear convection-diffusion-reaction equations range from parabolic to almost hyperbolic, depending on the ratio between convection and diffusion coefficients. From a numerical point of view, two main difficulties can arise related to the existence of layers and/or the non-smo...
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| Other Authors: | , |
| Format: | article |
| Language: | eng |
| Published: |
2009
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10316/11146 |
| Country: | Portugal |
| Oai: | oai:estudogeral.sib.uc.pt:10316/11146 |
| Summary: | In certain cases, quasilinear convection-diffusion-reaction equations range from parabolic to almost hyperbolic, depending on the ratio between convection and diffusion coefficients. From a numerical point of view, two main difficulties can arise related to the existence of layers and/or the non-smoothness of the coefficients of such equations. In this paper we study the steady-state solution of a convection-dominated problem. We present a new numerical method based on the idea of solving an associated modified problem, whose solution corresponds to a lifting of the solution of the initial problem. The method introduced here avoids an a priori knowledge of the layer(s) location and allows an efficient handling of the lack of smoothness of the coefficients. Numerical simulations that show the effectiveness of our approach are included. |
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