The finite element method with weighted basis functions for singularly perturbed convection-diffusion problems
A convection diffusion equation containing a small parameter at the high order derivative is considered. A finite element method using specially designed basis functions is proposed. These basis functions are obtained by means of multiplying the standard basis functions by a suitable weight. Properties of the basis functions are studied in one and two dimensions. Based on the properties of these basis functions a special technique is developed for approximating of fluxes. The approximate fluxes are used in the computation of the stiffness matrix in order to reduce the computational cost. Numerical results are given in one and two space dimensions.
scientific article; zbMATH DE number 2083223
scientific article