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Superconvergence error estimates for the div least-squares finite element method on elliptic problems (2404.04918v1)
Published 7 Apr 2024 in math.NA and cs.NA
Abstract: In this paper we discuss the error estimations for the div least-squares finite element method on elliptic problems. Compared with the previous work, we present a complete error analysis, which improves the current \emph{state-of-the-art} results. The error estimations for both the scalar and the flux variables are established by dual arguments, and in most cases, only an $H{1+\varepsilon}$ regularity is used. Numerical experiments strongly confirm our analysis.