Sociedad Colombiana de Matemáticas:Publicaciones

Revista Colombiana de Matemáticas

Volumen 34 [1] (2000)Páginas 1-18

A method of discretization for the Lagerström-Cole model equation

Fernando Usón Forniés
Universidad de Zaragoza, ESPAÑA (Spain)

Abstract. A method of discretization for a non linear singularly perturbed boundary value problem is considered. It involves a certain number of steps, one of them including the application of Petrov-Galerkin finite element methods. The resulting scheme is called adjoint method scheme and is in some way related to Niijima's scheme (cf. [11]). It is proved that this discretization provides existence and uniqueness of solution for a problem defined by the Lagerstr¨ om-Cole model equation. Finally some numerical experiments compare the results obtained when the adjoint method scheme is used, as well as when Niijima's scheme or a direct finite element discretization are applied.

Palabras claves. Singular perturbation problems, multigrid methods, finite elements, Petrov-Galerkin methods.

Codigo AMS. 1991 Primary 65N30. Secondary 65F10.

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