A numerical method for solving diffusion problems on polyhedral meshes is presented. It is based on a finite volume approximation with the degrees of freedom located in the centers of computational cells. A numerical gradient is defined by a least-squares minimization for each cell, where we suggest a restricted form in the case of discontinuous diffusion coefficient. The flux balanced approximation is proposed without numerically computing the gradient itself at the faces of computational cells in order to find a normal diffusive flux. To apply the method for parallel computations with a 1-ring neighborhood, we use an iterative method to solve the obtained system of algebraic equations. Several numerical examples illustrate some advantages of the proposed method.

中文翻译：

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多面体网格上扩散方程的最小二乘梯度通量平衡近似

提出了一种求解多面体网格扩散问题的数值方法。它基于有限的体积近似，自由度位于计算单元的中心。数字梯度由每个单元的最小二乘最小化定义，在不连续扩散系数的情况下，我们建议采用受限形式。提出了通量平衡近似，而不用数值计算计算单元表面上的梯度本身来找到正常的扩散通量。为了将该方法用于具有1环邻域的并行计算，我们使用迭代方法来求解所获得的代数方程组。几个数值例子说明了所提出方法的一些优点。