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arXiv · 2210.12116

Error analysis for a Crouzeix-Raviart approximation of the $p$-Dirichlet problem

Alex Kaltenbach
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Abstract

In the present paper, we examine a Crouzeix-Raviart approximation for non-linear partial differential equations having a $(p,δ)$-structure for some $p\in (1,\infty)$ and $δ\ge 0$. We establish a priori error estimates, which are optimal for all $p\in (1,\infty)$ and $δ\ge 0$, medius error estimates, i.e., best-approximation results, and a primal-dual a posteriori error estimate, which is both reliable and efficient. The theoretical findings are supported by numerical experiments.

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Alex Kaltenbach. 2024-06-07. Error analysis for a Crouzeix-Raviart approximation of the $p$-Dirichlet problem. https://doi.org/10.1515/jnma-2022-0106

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