A Class of Petrov-Galerkin Schemes for Singularly Perturbed Parabolic Problems with Discontinuous Convection Coefficients

摘要

In this paper, a class of singularly perturbed parabolic problems with discontinuous coefficients of the first space derivative is considered. These problems have turning points and weak interior layers near the discontinuous data. A class of difference schemes is generated by Petrov-Galerkin methods, which is exponentially fitted in the x -direction and classical differencing in the t -direction. In order to approximate the discontinuous data, a special technique is used. In this way we successfully deal with the discontinuous data. The class of Petrov-Galerkin schemes is proven to be first-order uniformly convergent in both t and x direction with equidistant partition under a Courant-Friedrichs-Lewy-type condition.