MESHLESS COLLOCATION METHODS WITH GRAPH LAPLACIAN FOR PDES ON FOLDED SURFACE

This work aims to provide a numerical treatment to deal with PDEs on surfaces with singularity along smooth curves. Previously, we proposed a low-order localized meshless method for discretizing the surface Laplacian operator on surfaces with folded. It is observed that the previously proposed strategy of approximating surface Laplacian at fold does not work with a recently developed high-order embedding meshless method for smooth surface. In this paper, we propose using the graph Laplacian to handel the surface singularity and study how it can be used to solve PDEs on folded surfaces.