Error analysis for a Crouzeix-Raviart approximation of the variable exponent Dirichlet problem
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In the present paper, we examine a Crouzeix-Raviart approximation for non-linear partial differential equations having a (p(·),δ)-structure. We establish a medius error estimate, i.e., a best-approximation result, which holds for uniformly continuous exponents and implies a priori error estimates, which apply for Hölder continuous exponents and are optimal for Lipschitz continuous exponents. The theoretical findings are supported by numerical experiments.
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