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Title: Lifting solutions of quasilinear convection-dominated problems
Authors: Ferreira, J. A. 
Mouro, A. P. 
Oliveira, P. 
Keywords: Convection-dominated problem; Non-uniform meshes; Convergence
Issue Date: 30-Apr-2009
Publisher: Taylor & Francis
Citation: International Journal of Computer Mathematics. (2009) iFirst
Abstract: 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.
ISSN: 0020-7160
DOI: 10.1080/00207160802385800
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Internacionais

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