Department of Mathematics
We analyze a least-squares strong-form kernel collocation formulation for solving second-order elliptic PDEs on smooth, connected, and compact surfaces with bounded geometry. The methods do not require any partial derivatives of surface normal vectors or metric. Based on some standard smoothness assumptions for high-order convergence, we provide the sufficient denseness conditions on the collocation points to ensure the methods are convergent. In addition to some convergence verifications, we also simulate some reaction-diffusion equations to exhibit the pattern formations.
mesh-free method, Kansa method, radial basis function, overdetermined collocation, narrowband method
Source Publication Title
SIAM Journal on Numerical Analysis
Society for Industrial and Applied Mathematics
Copyright © 2018, Society for Industrial and Applied Mathematics
This work was partially supported by a Hong Kong Research Grant Council GRF Grant, a Hong Kong Baptist University FRG Grant, and the National Natural Science Foundation of China (11528205).
Link to Publisher's Edition
Cheung, K., & Ling, L. (2018). A Kernel-based embedding method and convergence analysis for surfaces PDEs. SIAM Journal on Numerical Analysis, 40 (1), A266-A287. https://doi.org/10.1137/16M1080410