Lifting solutions of quasilinear convection-dominated problems

• Author(s): Ferreira, J. A. ; Mouro, A. P. ; Oliveira, P.
• Date: 2009
• Persistent ID: http://hdl.handle.net/10316/11146
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Convection-dominated problem; Non-uniform meshes; Convergence
• Document Type: Article
• Language: English

Description

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. http://dx.doi.org/10.1080/00207160802385800