doi:10.1016/j.apnum.2020.12.013engGracia, J.L.O'Riordan, E.Parameter-uniform approximations for a singularly perturbed convection-diffusion problem with a discontinuous initial conditionART-2021-122240A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified which matches the discontinuity in the initial condition. The difference between this analytical function and the solution of the parabolic problem is approximated numerically. A coordinate transformation is used so that a layer-adapted mesh can be aligned to the interior layer present in the solution. Numerical analysis is presented for the associated numerical method, which establishes that the numerical method is a parameter-uniform numerical method. Numerical results are presented to illustrate the pointwise error bounds established in the paper.2021http://zaguan.unizar.es/record/13080110.1016/j.apnum.2020.12.013http://zaguan.unizar.es/record/130801oai:zaguan.unizar.es:130801info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17Rinfo:eu-repo/grantAgreement/ES/MINECO-MCIU/PGC2018-094341-B-I00info:eu-repo/grantAgreement/ES/MINECO-MCIU/PID2019-105979GB-I00APPLIED NUMERICAL MATHEMATICS 162 (2021), 106-123by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess