Error analysis for a Crouzeix-Raviart approximation of the variable exponent Dirichlet problem

Abstract

In the present paper, we examine a Crouzeix-Raviart approximation of the $p(\cdot )$-Dirichlet problem. We derive a $\text{medius}$ error estimate, $\text{i.e.}$, a best-approximation result, which holds for uniformly continuous exponents and implies $\text{a priori}$ error estimates, which apply for Hölder continuous exponents and are optimal for Lipschitz continuous exponents. Numerical experiments are carried out to review the theoretical findings.

30 pages, 4 tables, this article extends the methods in arXiv:2210.12116 to the variable exponent setting