Matrix‐valued radial basis functions for the Lamé system

The problem of finding an approximate particular solution of an elliptic system of partial differential equations is considered. To construct the approximation, the differential operator is applied to a vector of radial basis functions. The resulting vectors are linearly combined to interpolate the function on the right hand side. The solvability of the interpolation problem is established. Additionally, stability, and accuracy estimates for the method are given. These theoretical results are illustrated on several numerical examples related to the Lamé system.