二维瞬态热传导问题的无单元Galerkin法分析

The element-free Galerkin (EFG) method was introduced to solve 2D transient heat conduction problems. Firstly, with the 2nd-order BDF scheme to address the time derivative term, the original problem was transformed into a series of time-independent mixed boundary value problems. Then, the penalty method was adopted to treat the Dirichlet boundary condition, and the element-free Galerkin method was established for 2D transient heat conduction problems. Finally, based on the error results of the moving least squares approximation, the error estimation of the element-free Galerkin method for 2D transient heat conduction problems was derived in detail. Numerical examples show that, the calculation results are in good agreement with the analytical solutions or the existing numerical solutions, and the EFG method has higher calculation accuracy and better convergence.