Construction and Convergence Study of Schemes Preserving the Elliptic Local Maximum Principle
Construction and Convergence Study of Schemes Preserving the Elliptic Local Maximum Principle
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DOI：
10.1137/090770849
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发表时间：
2011-03
期刊：
影响因子：
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通讯作者：
J. Droniou;C. L. Potier
中科院分区：
文献类型：
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作者：
J. Droniou;C. L. Potier
我们提出了一种方法来近似（在任何空间维度）扩散方程的计划具有特定的结构，这种结构确保离散的局部最大值和最小值的原则得到尊重，并且没有寄生振荡出现在解决方案。当应用于浓度方程模型的瞬态设置时，特别是近似解保持在物理边界之间。我们对所构造的格式进行了理论研究，证明了在有限性假设下，它们的解收敛于偏微分方程的解。还提供了几个数值结果，他们帮助我们了解如何选择的方法的参数。这些结果也表明了该方法的实际效率，即使在应用于复杂的模型。
We present a method to approximate (in any space dimension) diffusion equations with schemes having a specific structure; this structure ensures that the discrete local maximum and minimum principles are respected, and that no spurious oscillations appear in the solutions. When applied in a transient setting on models of concentration equations, it guaranties in particular that the approximate solutions stay between the physical bounds. We make a theoretical study of the constructed schemes, proving under a coercivity assumption that their solutions converge to the solution of the PDE. Several numerical results are also provided; they help us understand how the parameters of the method should be chosen. These results also show the practical efficiency of the method, even when applied to complex models.