Resumen de Convergencia uniforme de orden alto con interpolación sobre mallas de Shishkin

José Luis Gracia Lozano, Carmelo Clavero Gracia

• The pointwise uniform convergence of finite difference schemes defined on non uniform Shishkin meshes, used to solve singularly perturbed problems, is well known. In this work, we prove that it is possible to obtain uniform convergence in the complete domain, if we use an appropriate polynomial interpolation based on the solution in the mesh points. We show some numerical experiments confirming the theoretical results.