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Global-element-based free element method for solving non-linear and inhomogeneous heat conduction problems. (English) Zbl 07127495
Summary: In this paper, a family of global elements (GEs) are constructed for modeling geometries and representing physical variables, based on a set of complete basis functions formulated in terms of normalized global coordinates. The main benefits of using GEs are that the elemental nodes can be distributed and numbered in an arbitrary manner and the global spatial partial derivatives of geometries and physical variables appearing in the governing equations of engineering problems can be directly derived. Based on the constructed GEs and their spatial derivatives of global shape functions, a simple and robust new numerical method, called as the Global-Element-based FRee Element Method (GEFREM), is proposed for solving general two-dimensional heat conduction problems. GEFREM inherits the advantages of the finite element method, mesh free method and free element method. A detailed description of GEFREM for solving general non-linear and inhomogeneous heat conduction problems will be presented in the paper and a number examples are given to verify the correctness and demonstrate the potential of the proposed method.

MSC:
80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
80A10 Classical and relativistic thermodynamics
74F05 Thermal effects in solid mechanics
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