Numerical solution of transient heat conduction problems using improved meshless local Petrov–Galerkin method

An improved meshless local Petrov–Galerkin (MLPG) method is presented and applied to calculate the two-dimensional unsteady state heat conduction problems. In this method, the moving Kriging interpolation is employed instead of the traditional MLS approximation to construct the MLPG shape functions which possess Kronecker delta function property and thus make it easy to implement essential boundary conditions and then, the Heaviside step function is used as the test function over a local sub-domain. Since no mesh is needed either for integration of the local weak form, or for construction of the shape functions, the presently developed MLPG method is a truly meshless method. Several examples are performed to illustrate the accuracy and efficiency of the present method. A good agreement can be found among the proposed, analytical and finite element methods.