TY - JOUR
T1 - The Partition of Unity Method for High-Order Finite Volume Schemes Using Radial Basis Functions Reconstruction
AU - Serena Morigi & Fiorella Sgallari
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 153
EP - 179
PY - 2009
DA - 2009/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/nmtma/6020.html
KW - Finite volume discretization, radial basis functions, optimal recovery, regularization,
image and surface denoising.
AB - <p style="text-align: justify;">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.</p>