In the present paper, we examine a Crouzeix-Raviart approximation for non-linear partial differential equations having a $(p(\cdot),\delta)$-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 H\"older continuous exponents and are optimal for Lipschitz continuous exponents. The theoretical findings are supported by numerical experiments.
翻译:在本文中,我们研究了Crouzeix-Raviart逼近在具有$(p(\cdot),\delta)$-结构的非线性偏微分方程中的应用。我们建立了中等误差估计,即最优逼近结果,它适用于一致连续的指数,对于Hölder连续的指数则具有先验误差估计性质,并且对于Lipschitz连续的指数是最优的。理论结果得到了数值实验的证实。