In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.

中文翻译：

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非线性椭圆问题二次有限体积法的后验误差分析

在本文中，我们构造并分析了二次有限体积法 (FVM) 的基于残差的后验误差估计器，用于求解具有齐次 Dirichlet 边界条件的非线性椭圆偏微分方程。我们将证明后验误差估计量产生FVM 范数误差的全局上限和局部下限。使得后验误差估计量在某种意义上等同于真实误差。进行数值实验以说明理论结果。