Numerical solving of singularly perturbed boundary value problems with discontinuities

Helena Zarin, Snežana Gordić

One-dimensional convection-diffusion problem with interior layers caused by the discontinuity of data is considered. Though standard Galerkin finite element method (FEM) generates oscillations in the numerical solutions, we prove its convergence in the $\varepsilon$-weighted norm of the first order on a class of layer-adapted meshes. We use streamline-diffusion finite element method (SDFEM) in order to stabilize Galerkin FEM and prove $\varepsilon$-uniform convergence of the second order.