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 H¹ 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.
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Bertoluzza et al. (2024) studied this question.
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