The Partition of Unity Method for High-Order Finite Volume Schemes Using Radial Basis Functions Reconstruction

Abstract

This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equations. The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions. The methodology proposed is applied to the noise removal problem in functional surfaces and images. Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.