We analyze the local accuracy of the virtual element method. More precisely, we prove an error bound similar to the one holding for the finite element method, namely, that the local $H^1$ error in a interior subdomain is bounded by a term behaving like the best approximation allowed by the local smoothness of the solution in a larger interior subdomain plus the global error measured in a negative norm.

翻译：我们分析了虚元方法的局部精度。更精确地说，我们证明了与有限元方法类似的误差界，即内部子域上的局部$H^1$误差由一项表示，该项行为类似于由更大内部子域中解的局部光滑性所允许的最佳逼近，再加上以负范数度量的全局误差。