By using the improved moving least-square (IMLS) approximation to present the shape function, the improved element-free Galerkin (IEFG) method is investigated to solve diffusional drug release problems in this paper. In order to get the discretized equation system, Galerkin weak form of a diffusional drug release problem is used with applying essential boundary conditions using the penalty method. The difference method is applied for discretization of time domain. Then the formulae of IEFG method for solving diffusional drug release problems are presented. Three numerical example problems are given to study the convergence of solutions of IEFG method in this paper. The influences of scale parameters of influence domain, penalty factor and node distribution on the accuracy of the solutions of IEFG method are discussed. Compared with finite element method, the correctness of IEFG method in this paper is shown.

中文翻译：

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用于扩散药物释放问题的改进的无元素 Galerkin 方法

本文通过使用改进的移动最小二乘（IMLS）近似来表示形函数，研究改进的无元素伽辽金（IEFG）方法来解决扩散药物释放问题。为了得到离散化的方程组，利用惩罚方法应用基本边界条件，使用扩散药物释放问题的Galerkin弱形式。差分法用于时域的离散化。然后给出了IEFG法求解扩散药物释放问题的公式。本文给出了三个数值算例来研究IEFG方法解的收敛性。讨论了影响域尺度参数、惩罚因子和节点分布对IEFG方法解精度的影响。