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Numerical solution of transient heat conduction problems using improved meshless local Petrov-Galerkin method. (English) Zbl 1307.80008
A new formulation of the improved meshless local Petrov-Galerkin method is successfully applied to transient heat conduction problems. This approach is in the use of moving Kriging interpolation as the trail function, therefore, the essential boundary conditions can be enforced as the finite element method, and the Heaviside step function as the test function of the local weighted residual method. Some test problems are presented.

##### MSC:
 80M25 Other numerical methods (thermodynamics) (MSC2010) 80A20 Heat and mass transfer, heat flow (MSC2010) 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
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