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Error analysis for a Crouzeix-Raviart approximation of the variable exponent Dirichlet problem (2303.10687v4)
Published 19 Mar 2023 in math.NA and cs.NA
Abstract: In the present paper, we examine a Crouzeix-Raviart approximation of the $p(\cdot)$-Dirichlet problem. We derive a $\textit{medius}$ error estimate, $\textit{i.e.}$, a best-approximation result, which holds for uniformly continuous exponents and implies $\textit{a priori}$ error estimates, which apply for H\"older continuous exponents and are optimal for Lipschitz continuous exponents. Numerical experiments are carried out to review the theoretical findings.
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