Abstract It is still an open problem to prove a priori error estimates for finite volume schemes of higher order MUSCL type, including limiters, on unstructured meshes, which show some improvement compared to first order schemes. In this paper we use these higher order schemes for the discretization of convection dominated elliptic problems in a convex bounded domain Ω in ℝ2 and we can prove such kind of an a priori error estimate. In the part of the estimate, which refers to the discretization of the convective term, we gain h1/2. Although the original problem is linear, the numerical problem becomes nonlinear, due to MUSCL type reconstruction/limiter technique.

中文翻译：

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对流扩散问题的高阶有限体积方案的误差估计

摘要 在非结构化网格上证明高阶 MUSCL 类型的有限体积方案（包括限制器）的先验误差估计仍然是一个悬而未决的问题，与一阶方案相比，这些方案显示出一些改进。在本文中，我们将这些高阶方案用于 ℝ2 中凸有界域 Ω 中对流主导椭圆问题的离散化，并且我们可以证明这种先验误差估计。在估计部分，即对流项的离散化，我们得到 h1/2。尽管原始问题是线性的，但由于 MUSCL 类型的重建/限制器技术，数值问题变成了非线性问题。