A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data
A numerical method is suggested for singularly perturbed boundary-value problems with finite jump discontinuity in the convection coefficient, and the source term at an interior point. Because of the discontinuity in the data, these problems possess an interior layer in addition to the boundary layers. Here, the authors propose a Petrov-Galerkin finite element method with piecewise-exponential test functions and piecewise-linear trial functions. The point of discontinuity of the coefficient is handled carefully. First-order \(\varepsilon\)-uniform error estimates are proved. A numerical example is carried out to verify the theoretical results.
scientific article; zbMATH DE number 5076955