A MESHLESS METHOD BASED ON LEAST-SQUARES APPROACH FOR STEADY- AND UNSTEADY-STATE HEAT CONDUCTION PROBLEMS

The meshless method based on the least-squares approach, the meshless weighted least-squares (MWLS) method, is extended to solve conduction heat transfer problems. The MWLS formulation is first established for steady-state problems and then extended to unsteady-state problems with time-stepping schemes. Theoretical analysis and numerical examples indicate that larger time steps can be used in the present method than in meshless methods based on the Galerkin approach. Numerical studies show that the proposed method is a truly meshless method with good accuracy, high convergence rate, and high efficiency.