Abstract
AbstractWe present an error bound for a least squares version of the kernel based meshless finite difference method for elliptic differential equations on smooth compact manifolds of arbitrary dimension without boundary. In particular, we obtain sufficient conditions for the convergence of this method. Numerical examples are provided for the equation$$-\Delta _{\mathcal {M}} u + u = f$$-ΔMu+u=fon the 2- and 3-spheres, where$$\Delta _{\mathcal {M}} $$ΔMis the Laplace-Beltrami operator.
Funder
Justus-Liebig-Universität Gießen
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics
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