doi:10.1016/j.apnum.2019.08.005engGracia, J.L.O''Riordan, E.Parameter-uniform numerical methods for singularly perturbed parabolic problems with incompatible boundary-initial dataART-2019-114760Numerical approximations to the solution of a linear singularly perturbed parabolic reaction-diffusion problem with incompatible boundary-initial data are generated. The method involves combining the computational solution of a classical finite difference operator on a tensor product of two piecewise-uniform Shishkin meshes with an analytical function that captures the local nature of the incompatibility. A proof is given to show almost first order parameter-uniform convergence of these numerical/analytical approximations. Numerical results are given to illustrate the theoretical error bounds.2019http://zaguan.unizar.es/record/13077210.1016/j.apnum.2019.08.005http://zaguan.unizar.es/record/130772oai:zaguan.unizar.es:130772info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17Rinfo:eu-repo/grantAgreement/ES/MCYT-FEDER/MTM2016-75139-RAPPLIED NUMERICAL MATHEMATICS 146 (2019), 436-451All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess