A technique for generating adapted discretizations to solve partial differential equations with the generalized finite difference method

Abstract

The generalized finite difference method is a meshless method for solving partial differential equations that allows arbitrary discretizations of points. Typically, the discretizations have the same density of points in the domain. We propose a technique to get adapted discretizations for the solution of partial differential equations. This strategy allows using a smaller number of points and, therefore, a lower computational cost, to achieve the same accuracy that would be obtained with a regular discretization. KEYWORDSadapted discretization, fourth-order approximations, generalized finite difference method MSC CLASSIFICATION 65M06, 65M50Miguel Ureña, PhD, contributed to this article in his personal capacity. The views expressed are his own and do not necessarily represent the views of Statistics Spain.