MLPG solution of elliptic PDE

Meshless methods for the numerical solution of Partial Differential Equations (PDE) are emerging techniques. Nowadays their efficiency is not comparable to Finite Element methods. Among the ample literature on meshless methods, we focus on Meshless Petrov--Galerkin (MLPG) methods.In many variants they pervade the Research on meshless methods for solving PDE. This thesis aims at implementing a MATLAB code allowing for the numerical approximation of Poisson problems. The accuracy and efficiency of the code is tested. Moreover, strategies for using GPU devices are analyzed, developed and implemented. A discussion of the their efficiency is conducted on test problems.