Mesh-free mixed finite element approximation for nonlinear time-fractional biharmonic problem using weighted b-splines
Authors :- Mandaliya, J.P.; Kumar, D.; Chaudhary, S.
Publication :- International Journal of Computer Mathematics, Dec 2025 (Taylor & Francis).
In this article, we propose a fully-discrete scheme for the numerical solution of a nonlinear time-fractional biharmonic problem. This problem is first converted into an equivalent system by introducing a new variable. Then spatial and temporal discretizations are done by the weighted b-spline method and 𝐿2-1𝜎 approximation, respectively. The weighted b-spline method uses weighted b-splines on a tensor product grid as basis functions for the finite element space and by construction, it is a mesh-free method. This method combines the computational benefits of b-splines and standard mesh-based elements. We derive α-robust a priori bound and convergence estimate in the 𝐿2(Ω) norm for the proposed scheme. Finally, we carry out a few numerical experiments to support our theoretical findings.