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A two-grid method for the semi-linear reaction-diffusion system of the solutes in the groundwater flow by finite volume element

机译:有限体积元法求解地下水中溶质的半线性反应扩散系统的两网格方法

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Based on two different spaces defined on one coarse grid with mesh size H and one fine grid with mesh size h, a two-grid finite volume method is introduced to obtain the solutions of semi-linear reaction-diffusion equations of the solutes in the groundwater flow. The standard finite element Ritz projection and elliptic projection are applied to the analysis of this approach. Error estimates in L~2 norm and H~1 norm are derived in this paper. The above estimates can be applied to choose H = O(h~(1/4)) in the H~1 norm and H = O(h~(1/2)) in the L~2 norm for the coarse grid problems. Some numerical examples are presented to justify the efficiency and accuracy of the method.
机译:基于在一个网格尺寸为H的粗网格和一个网格尺寸为h的细网格上定义的两个不同空间,提出了一种两网格有限体积方法来获得地下水中溶质的半线性反应扩散方程的解。流。将标准有限元Ritz投影和椭圆投影应用于此方法的分析。本文推导了L〜2范数和H〜1范数的误差估计。对于粗网格问题,以上估计可用于选择H〜1范式中的H = O(h〜(1/4))和L〜2范式中的H = O(h〜(1/2)) 。给出了一些数值例子来证明该方法的效率和准确性。

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