Numerical assessment regarding the time-dependent heat conduction equation using Meshless Local Petrov-Galerkin and Radial Point Interpolation Method

This study presents and evaluates four distinct case studies concerning the transient (unsteady) heat conduction equation. The Meshless Local Petrov-Galerkin (MLPG) method is employed, and a direct comparison is performed between the distinct approximation functions: the Moving Least-Squares (MLS), the Radial Point Interpolation Method (RPIM) and the Interpolating Moving Least-Squares(IMLS). The first numerical example investigates a more complex two-dimensional geometry, specifically a quarter