165233 20251219174252.0 doi 10.1007/s11075-025-02247-x sideral 147007 ART-2025-147007 eng Meng, Xiangyun Local analysis of an L1/finite element method for a time-fractional singularly perturbed reaction-diffusion problem 2025 An initial-boundary value problem of the form is considered on the space-time domain , with Dirichlet boundary and initial conditions, where is a Caputo fractional derivative of order and the singular perturbation parameter is a positive constant. Bounds on the solution u and its derivatives are proved by means of a comparison principle with a careful selection of barrier functions; it is seen that u has a weak singularity at the initial time (caused by the fractional derivative) and also has layers (caused by the small parameter ) at the sides of the space-time domain. The Caputo derivative is discretised by the L1 scheme on a graded temporal mesh, then at each time level the PDE is discretised by a piecewise linear finite element method on a Shishkin spatial mesh. Using our bounds on the derivatives of u, error estimates for the computed solution are derived in , energy and balanced norms on [0, 1] for each t; these estimates are local in time and uniform in . Numerical experiments show the sharpness of our theoretical results. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/DGA/E24-23R info:eu-repo/grantAgreement/ES/MICINN/PID2022-141385NB-I00 info:eu-repo/semantics/embargoedAccess All rights reserved http://www.europeana.eu/rights/rr-f/ info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Gracia, José Luis Universidad de Zaragoza (orcid)0000-0003-2538-9027 Stynes, Martin 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada (2025), [36 pp.] Numer. algorithms NUMERICAL ALGORITHMS 1017-1398 2422730 http://zaguan.unizar.es/record/165233/files/texto_completo.pdf Versión publicada info:eu-repo/date/embargoEnd/2026-12-09 1978054 http://zaguan.unizar.es/record/165233/files/texto_completo.jpg?subformat=icon icon Versión publicada info:eu-repo/date/embargoEnd/2026-12-09 oai:zaguan.unizar.es:165233 articulos driver 2025-12-19-14:43:30 ARTICLE