Meshless Finite Difference Methods

After a brief discussion of the motivations and some history of the generalized finite difference methods, the speaker will concentrate on their recent meshless versions relying on kernel based numerical differentiation on irregular centers. Consistency estimates for such methods have been recently obtained in [1], whereas numerically successful adaptive algorithms for elliptic equations developed in [2-4].

1. Oleg Davydov and Robert Schaback, Error bounds for kernel-based numerical differentiation, Numer. Math., 132 (2016), 243-269.
2. Oleg Davydov and Dang Thi Oanh, Adaptive meshless centres and RBF stencils for Poisson equation, J. Comput. Phys., 230 (2011), 287-304.
3. Oleg Davydov and Dang Thi Oanh, On optimal shape parameter for Gaussian RBF-FD approximation of Poisson equation, Comput. Math. Appl., 62 (2011), 2143--2161.
4. Dang Thi Oanh, Oleg Davydov and Hoang Xuan Phu, Adaptive RBF-FD methods for elliptic problems with point singularities in 2D, preprint, 2016. arXiv:1603.07838