This paper deals with the solution of the pure Neumann problem for the diffusion equation by a finite element method. First, an extended generalized formulation of the Neumann problem in the Sobolev space H¹(Ω) is derived and investigated. Then a discrete analog of this problem is formulated by using standard finite element approximations of the space H¹(Ω). An iterative method for solving the corresponding SLAE is proposed. Some examples of solving model problems are used to discuss the numerical properties of the algorithm proposed.

中文翻译：

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用有限元方法求解纯诺伊曼问题

本文用有限元方法解决了扩散方程的纯诺伊曼问题。首先，推导并研究了Sobolev空间H ¹（Ω）中Neumann问题的扩展广义公式。然后，通过使用空间H ¹（Ω）的标准有限元逼近来公式化此问题的离散模拟。提出了一种求解相应SLAE的迭代方法。一些解决模型问题的例子被用来讨论所提出算法的数值性质。