000165233 001__ 165233
000165233 005__ 20251219174252.0
000165233 0247_ $$2doi$$a10.1007/s11075-025-02247-x
000165233 0248_ $$2sideral$$a147007
000165233 037__ $$aART-2025-147007
000165233 041__ $$aeng
000165233 100__ $$aMeng, Xiangyun
000165233 245__ $$aLocal analysis of an L1/finite element method for a time-fractional singularly perturbed reaction-diffusion problem
000165233 260__ $$c2025
000165233 5060_ $$aAccess copy available to the general public$$fUnrestricted
000165233 5203_ $$aAn 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.
000165233 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E24-23R$$9info:eu-repo/grantAgreement/ES/MICINN/PID2022-141385NB-I00
000165233 540__ $$9info:eu-repo/semantics/embargoedAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000165233 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000165233 700__ $$0(orcid)0000-0003-2538-9027$$aGracia, José Luis$$uUniversidad de Zaragoza
000165233 700__ $$aStynes, Martin
000165233 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000165233 773__ $$g(2025), [36 pp.]$$pNumer. algorithms$$tNUMERICAL ALGORITHMS$$x1017-1398
000165233 8564_ $$s2422730$$uhttps://zaguan.unizar.es/record/165233/files/texto_completo.pdf$$yVersión publicada$$zinfo:eu-repo/date/embargoEnd/2026-12-09
000165233 8564_ $$s1978054$$uhttps://zaguan.unizar.es/record/165233/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada$$zinfo:eu-repo/date/embargoEnd/2026-12-09
000165233 909CO $$ooai:zaguan.unizar.es:165233$$particulos$$pdriver
000165233 951__ $$a2025-12-19-14:43:30
000165233 980__ $$aARTICLE