A mixed method for Dirichlet problems with radial basis functions
Norbert Heuer and Thanh Tran
Comput. Math. Appl. 66 (10), 2045-2055, 2013.
We present a simple discretization by radial basis functions
for the Poisson equation with Dirichlet boundary condition.
A Lagrangian multiplier using piecewise polynomials
is used to accommodate the boundary condition. This
simplifies previous attempts to use radial basis functions
in the interior domain to approximate the solution
and on the boundary to approximate the multiplier,
which technically requires that the mesh norm in the interior
domain is significantly smaller than that on the boundary.
Numerical experiments confirm theoretical results.