• meshless MLPG1 and MLPG5 methods;
  • jump function;
  • Lagrange multipliers;
  • convergence studies


We use two meshless local Petrov–Galerkin (MLPG) formulations to analyse heat conduction in a bimetallic circular disk. The continuity of the normal component of the heat flux at the interface between two materials is satisfied either by the method of Lagrange multipliers or by using a jump function. The convergence of the H0 and H1 error norms for the four numerical solutions with an increase in the number of equally spaced nodes and in the number of quadrature points is scrutinized. With an increase in the number of uniformly spaced nodes, the two error norms decrease monotonically for the MLPG5 formulation but are essentially unchanged for the MLPG1 formulation. To our knowledge, this is the first study comparing the performance of the two methods of modelling a discontinuity in the gradient of a field variable at the interface between two different materials. Copyright © 2004 John Wiley & Sons, Ltd.