The characteristic RBF-FD method for the convection-diffusion-reaction equation on implicit surfaces

Abstract

In this article, a characteristic radial basis function-generated finite differences method (RBF-FD) is presented to numerically solve the convection-diffusion-reaction equation on implicit surfaces. By the method of characteristics, the convection-diffusion-reaction equation can be transformed into diffusion-type equation so that RBF-FD method only need to discretize the surface Laplacian operator. The theoretical estimate of error bounds in terms of interpolation is obtained. Finally, numerical examples are presented to show the convergence and efficiency of the characteristic RBF-FD method on implicit surfaces.