Resumen: Numerical approximations to the solution of a linear singularly perturbed parabolic convection-diffusion problem are generated using a backward Euler method in time and an upwinded finite difference operator in space on a piecewise-uniform Shishkin mesh. A proof is given to show first order convergence of these numerical approximations in an appropriately weighted C^1$-norm. Numerical results are given to illustrate the theoretical error bounds. Idioma: Inglés DOI: 10.1090/mcom/2998 Año: 2016 Publicado en: MATHEMATICS OF COMPUTATION 85, 298 (2016), 581-599 ISSN: 0025-5718 Factor impacto JCR: 1.569 (2016) Categ. JCR: MATHEMATICS, APPLIED rank: 47 / 255 = 0.184 (2016) - Q1 - T1 Factor impacto SCIMAGO: 1.872 - Algebra and Number Theory (Q1) - Computational Mathematics (Q1) - Applied Mathematics (Q1)