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首页> 外文期刊>Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology >Error estimation and adaptivity for finite-volume methods on unstructured triangular meshes: Elliptic heat transfer problems
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Error estimation and adaptivity for finite-volume methods on unstructured triangular meshes: Elliptic heat transfer problems

机译：非结构三角形网格上有限体积方法的误差估计和适应性：椭圆形传热问题

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摘要

In this article, a simple and reliable a posteriori error estimate methodology for the finite-volume method on triangular meshes and an adaptive mesh refinement procedure are presented. The proposed error estimate employs a high-order approximation for the scalar at the triangles faces. The estimate technique does not demand expressive computational efforts and memory storage. The adaptive procedure is based on the equal distribution of the error over all the triangles, allowing for suitable local mesh refinements. The error is measured by an H-1 norm, and its convergence behavior is evaluated using four elliptic problems for which the analytical solutions are known. The error differences using analytical and estimate solutions are compared for those problems, and good performance of the adaptive procedure is verified. [References: 21]
机译：在本文中，提出了一种简单可靠的三角网格有限体积方法的后验误差估计方法和自适应网格细化程序。拟议的误差估计对三角形面处的标量采用高阶近似。估计技术不需要表达性的计算工作和内存存储。自适应程序基于所有三角形上误差的均等分布，从而可以进行适当的局部网格细化。通过H-1范数测量误差，并使用四个椭圆问题评估其收敛行为，这些椭圆问题的解析解是已知的。比较了使用解析和估计解决方案的误差差异，并验证了自适应程序的良好性能。 [参考：21]

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