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:我们分析虚拟元素方法的局部精度。更确切地说,我们证明了一种类似于有限元方法的误差界限,即在内部子域中局部$H^1$误差受到一个类似于较大内部子域中解局部光滑度允许的最佳逼近加上在负范数中测量的全局误差的控制。