A Shishkin mesh based modified bi-cubic B-spline approach for two-dimensional elliptic convection-diffusion problems with regular boundary layers

Jangid, Hemlata ; Kumari, Parvin ; Clavero, Carmelo (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1007/s11075-026-02343-6

Año: 2026

Publicado en: NUMERICAL ALGORITHMS (2026), [25 pp.]
ISSN: 1017-1398

Financiación: info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R
Financiación: info:eu-repo/grantAgreement/ES/MCINN/PID2022-136441NB-I00

Tipo y forma: Article (Published version)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)