170213 20260407115449.0 doi 10.1007/s11075-026-02343-6 sideral 148746 ART-2026-148746 eng Jangid, Hemlata A Shishkin mesh based modified bi-cubic B-spline approach for two-dimensional elliptic convection-diffusion problems with regular boundary layers 2026 In this work, we construct a new numerical approach to solve two-dimensional elliptic singularly perturbed convection-diffusion problem (SPCDP) having regular boundary layers. The proposed approach combines the use of an adequate Shishkin mesh, which is specifically designed to resolve the type of regular boundary layers which appear in the exact solution, with a modified bi-cubic B-spline (MBCBS) collocation technique, that ensures high-order accuracy of the numerical method. Higher-order splines are particularly advantageous from a practical perspective, as it delivers accurate approximations without increase significantly the computational cost of the algorithm. A detailed analysis of error is performed, and therefore, the proposed method is proven to be a nearly second-order parameter uniformly convergent in the maximum norm. Numerical experiments are also provided to validate in practice the theoretical results and to corroborate the effectiveness and robustness of the proposed scheme on challenging test problems. info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R info:eu-repo/grantAgreement/ES/MCINN/PID2022-136441NB-I00 info:eu-repo/semantics/closedAccess All rights reserved http://www.europeana.eu/rights/rr-f/ info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Kumari, Parvin Clavero, Carmelo Universidad de Zaragoza (orcid)0000-0003-1263-1996 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada (2026), [25 pp.] Numer. algorithms NUMERICAL ALGORITHMS 1017-1398 4449412 http://zaguan.unizar.es/record/170213/files/texto_completo.pdf Versión publicada info:eu-repo/date/embargoEnd/2027-03-09 1212238 http://zaguan.unizar.es/record/170213/files/texto_completo.jpg?subformat=icon icon Versión publicada info:eu-repo/date/embargoEnd/2027-03-09 oai:zaguan.unizar.es:170213 articulos driver 2026-03-26-14:31:49 ARTICLE