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Application of meshless element-free Galerkin method in two-dimensional heat conduction problems. (English) Zbl 1101.80005
Summary: Meshless element free Galerkin method has been used to obtain the numerical solution of transient and steady state heat conduction problems in two-dimensional domains. The unknown function of temperature $$T({\mathbf x})$$ has been approximated by moving least square approximant $$T^h({\mathbf x})$$. These approximants are constructed by using a weight function, a polynomial basis and a set of non-constant coefficients. Variational method is used to obtain the discrete equations. Essential boundary conditions are imposed by Lagrange multiplier technique. Two new weight functions namely hyperbolic and rational have been proposed. The results have been obtained for a two-dimensional model problem using different EFG weight functions and are compared with those obtained by finite element and analytical methods.

##### MSC:
 80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer 80A20 Heat and mass transfer, heat flow (MSC2010)