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

2023/03/19 by Balci, Anna Kh., Kaltenbach, Alex
#35J60 #46E30 #49M29 #65N15 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2303.10687

Abstract

In the present paper, we examine a Crouzeix-Raviart approximation of the p(⋅)-Dirichlet problem. We derive 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. Numerical experiments are carried out to review the theoretical findings.

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